Manual for the Solution of Military Ciphers in Modern English

This is a modern-English version of Manual for the Solution of Military Ciphers, originally written by Hitt, Parker. It has been thoroughly updated, including changes to sentence structure, words, spelling, and grammar—to ensure clarity for contemporary readers, while preserving the original spirit and nuance. If you click on a paragraph, you will see the original text that we modified, and you can toggle between the two versions.

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MANUAL FOR THE SOLUTION OF MILITARY CIPHERS

BY
Parker Hitt
Captain of Infantry, U. S. A.

PRESS OF
THE ARMY SERVICE SCHOOLS
Fort Leavenworth, Kansas
1916

[v]

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MANUAL FOR THE SOLUTION
OF MILITARY CIPHERS

Manual for Decoding Military Codes

BY
PARKER HITT
Captain of Infantry, United States Army

Introduction

The history of war teems with occasions where the interception of dispatches and orders written in plain language has resulted in defeat and disaster for the force whose intentions thus became known at once to the enemy. For this reason, prudent generals have used cipher and code messages from time immemorial. The necessity for exact expression of ideas practically excludes the use of codes for military work although it is possible that a special tactical code might be useful for preparation of tactical orders.

The history of war is filled with instances where intercepting messages and orders written in plain language has led to defeat and disaster for the forces whose plans were immediately revealed to the enemy. Because of this, wise generals have relied on ciphers and codes for a long time. The need for precise communication practically rules out the use of codes for military operations, although a specialized tactical code might be helpful for preparing tactical orders.

It is necessary therefore to fall back on ciphers for general military work if secrecy of communication is to be fairly well assured. It may as well be stated here that no practicable military cipher is mathematically indecipherable if intercepted; the most that can be expected is to delay for a longer or shorter time the deciphering of the message by the interceptor.

It’s essential to use ciphers for military operations if we want to keep communication secret. It should also be noted that no military cipher is completely unbreakable if intercepted; the best we can hope for is to slow down the process of deciphering the message for whoever intercepts it.

The capture of messengers is no longer the only means available to the enemy for gaining information as to the plans of a commander. All radio messages sent out can be copied at hostile stations within radio range. If the enemy can get a fine wire within one hundred feet of a buzzer line or within thirty feet of a telegraph line, the message can be copied by induction. Messages passing over commercial telegraph lines, and even over military lines, can be copied by spies in the offices. On telegraph lines of a permanent nature it is possible to install high speed automatic sending and receiving machines and thus prevent surreptitious copying of messages, but nothing but a secure cipher will serve with other means of communication. [vi]

The capture of messengers isn't the only way for the enemy to gather information about a commander's plans anymore. Any radio messages sent out can be intercepted by hostile stations within radio range. If the enemy can place a fine wire within a hundred feet of a buzzer line or within thirty feet of a telegraph line, they can copy the message through induction. Messages sent over commercial telegraph lines and even military lines can be intercepted by spies in the offices. On permanent telegraph lines, it's possible to set up high-speed automatic sending and receiving machines to prevent unauthorized copying of messages, but only a secure cipher will work with other communication methods. [__A_TAG_PLACEHOLDER_0__]

It is not alone the body of the message which should be in cipher. It is equally important that, during transmission, the preamble, place from, date, address and signature be enciphered; but this should be done by the sending operator and these parts must, of course, be deciphered by the receiving operator before delivery. A special operators’ cipher should be used for this purpose but it is difficult to prescribe one that would be simple enough for the average operator, fast and yet reasonably safe. Some form of rotary cipher machine would seem to be best suited for this special purpose.

It’s not just the message itself that should be coded; it’s just as crucial that the preamble, sender’s location, date, address, and signature are also encrypted during transmission. However, this encryption should be handled by the sending operator, and these elements must be decrypted by the receiving operator before delivery. A specific cipher for operators should be used for this, but it’s challenging to find one that’s simple enough for the average operator while still being fast and reasonably secure. A type of rotary cipher machine seems to be the best fit for this specific need.

It is unnecessary to point out that a cipher which can be deciphered by the enemy in a few hours is worse than useless. It requires a surprisingly long time to encipher and decipher a message, using even the simplest kind of cipher, and errors in transmission of cipher matter by wire or radio are unfortunately too common.

It’s obvious that a cipher that the enemy can crack in a few hours is more harmful than helpful. It takes an unexpectedly long time to encode and decode a message, even with the simplest cipher, and mistakes in transmitting ciphered content over wire or radio are unfortunately too frequent.

Kerckhoffs has stated that a military cipher should fulfill the following requirements:

Kerckhoffs said that a military cipher should meet the following requirements:

1st. The system should be materially, if not mathematically, indecipherable.
2d. It should cause no inconvenience if the apparatus and methods fall into the hands of the enemy.
3d. The key should be such that it could be communicated and remembered without the necessity of written notes and should be changeable at the will of the correspondents.
4th. The system should be applicable to telegraphic correspondence.
5th. The apparatus should be easily carried and a single person should be able to operate it.
6th. Finally, in view of the circumstances under which it must be used, the system should be an easy one to operate, demanding neither mental strain nor knowledge of a long series of rules.

A brief consideration of these six conditions must lead to the conclusion that there is no perfect military cipher. The first requirement is the one most often overlooked by those prescribing the use of any given cipher and, even if not overlooked, the indecipherability of any cipher likely to be used for military purposes is usually vastly overestimated by those prescribing the use of it.

A quick look at these six conditions shows that there isn’t a flawless military cipher. The first requirement is the one that people most often ignore when recommending any specific cipher, and even when it's not ignored, the inability to decode any cipher intended for military use is usually greatly overestimated by those suggesting it.

If this were not true, there would have been neither material for, nor purpose in, the preparation of these notes. Of the hundreds of actual cipher messages examined by the writer, at least nine-tenths have been solved by the methods to be set forth. These messages were prepared by the methods in use by the United States Army, the various Mexican [vii]armies and their secret agents, and by other methods in common use. The usual failure has been with very short messages. Foreign works consulted lead to the belief that many European powers have used, for military purposes, cipher methods which vary from an extreme simplicity to a complexity which is more apparent than real. What effect recent events have had on this matter remains to be seen. It is enough that the cipher experts of practically every European country have appealed to the military authorities of their respective countries time and again to do away with these useless ciphers and to adopt something which offers more security, even at the expense of other considerations.

If this weren't true, there wouldn't be any material or purpose for creating these notes. Out of the hundreds of actual cipher messages the writer has examined, at least 90% have been solved using the methods that will be discussed. These messages were created using the techniques employed by the United States Army, various Mexican armies and their secret agents, as well as other commonly used methods. The usual failures have occurred with very short messages. Research on foreign works suggests that many European powers have utilized cipher methods for military purposes that range from extremely simple to complex, though the complexity is often more misleading than substantial. The impact of recent events on this issue is still unclear. It's enough to note that the cipher experts from nearly every European country have repeatedly urged their military authorities to eliminate these ineffective ciphers and switch to something that provides better security, even if it comes at the cost of other considerations.

The cipher of the amateur, or of the non-expert who makes one up for some special purpose, is almost sure to fall into one of the classes whose solution is an easy matter. The human mind works along the same lines, in spite of an attempt at originality on the part of the individual, and this is particularly true of cipher work because there are so few sources of information available. In other words, the average man, when he sits down to evolve a cipher, has nothing to improve upon; he invents and there is no one to tell him that his invention is, in principle, hundreds of years old. The ciphers of the Abbé Tritheme, 1499, are the basis of most of the modern substitution ciphers.

The code created by an amateur or a non-expert who comes up with one for a specific reason is likely to fall into a category that is easy to solve. The human mind tends to follow similar patterns, even if the individual tries to be original, and this is especially true with codes because there are so few references to draw from. In other words, when an average person sits down to create a code, they don't have anything to build on; they just invent, unaware that their creation is, in principle, hundreds of years old. The codes developed by Abbé Tritheme in 1499 form the foundation of most modern substitution codes.

In view of these facts, no message should be considered indecipherable. Very short messages are often very difficult and may easily be entirely beyond the possibility of analysis and solution, but it is surprising what can be done, at times, with a message of only a few words.

In light of these facts, no message should be seen as impossible to decode. Very short messages can often be quite challenging and might be completely beyond analysis and resolution, but it's surprising what can sometimes be accomplished with just a few words in a message.

In the event of active operations, cipher experts will be in demand at once. Like all other experts, the cipher expert is not born or made in a day; and it is only constant work with ciphers, combined with a thorough knowledge of their underlying principles, that will make one worthy of the name. [1]

In the case of active operations, cipher experts will be needed immediately. Like all other specialists, a cipher expert isn’t created overnight; it takes ongoing work with ciphers, along with a deep understanding of their foundational principles, to truly earn that title. [__A_TAG_PLACEHOLDER_0__]

Chapter I

Equipment for Cipher Work

Success in dealing with unknown ciphers is measured by these four things in the order named; perseverance, careful methods of analysis, intuition, luck. The ability at least to read the language of the original text is very desirable but not essential.

Success in tackling unknown ciphers is measured by these four things in the order listed: perseverance, careful analysis methods, intuition, and luck. Being able to read the original text's language is definitely helpful, but it's not a must.

Cipher work will have little permanent attraction for one who expects results at once, without labor, for there is a vast amount of purely routine labor in the preparation of frequency tables, the rearrangement of ciphers for examination, and the trial and fitting of letter to letter before the message begins to appear.

Cipher work won’t have much lasting appeal for anyone who expects immediate results without hard work because there’s a lot of tedious routine involved in creating frequency tables, rearranging ciphers for review, and testing and matching letters before the message starts to take shape.

The methods of analysis given in these notes cover only the simpler varieties of cipher and it is, of course, impossible to enumerate all the varieties of these. It is believed that the methods laid down are sound and several years of successful work along this line would seem to confirm this belief. For more advanced work there is no recourse but to study the European authorities whose writings are mostly in French, German, and Italian and, unfortunately, are rarely available in English translations.

The analysis methods presented in these notes only cover the simpler types of ciphers, and it's impossible to list all the different kinds. We believe the methods outlined are reliable, and several years of successful work in this area seem to support that belief. For more advanced studies, the only option is to refer to European experts, whose writings are mostly in French, German, and Italian, and unfortunately, are seldom available in English translations.

Under intuition must be included a knowledge of the general situation and, if possible, the special situation which led to the sending of the cipher message. The knowledge or guess that a certain cipher message contains a particular word, often leads to its solution. [2]

Under intuition, there should be an understanding of the overall context and, if feasible, the specific circumstances that prompted the transmission of the coded message. Knowing or inferring that a certain coded message includes a particular word often helps in deciphering it. [__A_TAG_PLACEHOLDER_0__]

As to luck, there is the old miner’s proverb: “Gold is where you find it.”

As for luck, there’s an old miner’s saying: “Gold is where you find it.”

The equipment for an office, where much cipher work is handled, will now be considered. The casual worker with ciphers can get along with much less, but the methods of filing and keeping a record of all messages studied should be followed wherever possible. The interchange of results between individuals and between offices should be encouraged and, in time of active operations, should be mandatory. An enemy may be using the same cipher in widely separated parts of the zone of operations and it is useless labor to have many cipher offices working on intercepted messages, all in the same cipher, when one office may have the solution that will apply to all of them.

The equipment for an office that handles a lot of cipher work will now be discussed. A casual worker dealing with ciphers can manage with much less, but it's important to follow the methods for filing and keeping a record of all analyzed messages whenever possible. Sharing results between individuals and offices should be encouraged and, during active operations, should be mandatory. An enemy might be using the same cipher in different parts of the operation area, and it's a waste of effort to have multiple cipher offices working on intercepted messages—all in the same cipher—when one office might have a solution that applies to all of them.

Cipher work requires concentration and quiet and often must proceed without regard to hours. The office should be chosen with these points in mind. A clerical force is desirable and even necessary if there is much work to do. The clerk or clerks can soon be trained to do the routine part of the analysis.

Cipher work needs focus and silence and often has to go on regardless of time. The workspace should be selected with these factors in mind. A team of clerks is helpful and even essential if there's a lot of work to be done. The clerk or clerks can quickly be trained to handle the routine aspects of the analysis.

It is believed that each Field Army should have such an office where all ciphers intercepted by forces under command of the Field Army Commander should be sent at once for examination. This work naturally falls to the Intelligence section of the General Staff at this headquarters. A special radio station, with receiving instruments only, should be an adjunct to this office and its function should be to copy all hostile radio messages whether in cipher or plain text. Such a radio station requires but a small antenna; one of the pack set type or any amateur’s antenna is sufficient, and the station instruments can be easily carried in a suit case. Three thoroughly competent operators should be [3]provided, so that the station can be “listening in” during the entire twenty-four hours.

It is believed that every Field Army should have an office where all ciphers intercepted by the forces under the command of the Field Army Commander can be sent immediately for analysis. This task naturally falls to the Intelligence section of the General Staff at this headquarters. A dedicated radio station, equipped only with receiving instruments, should be part of this office, and its role should be to copy all hostile radio messages, whether they are encrypted or in plain text. This radio station only needs a small antenna; a portable type or any amateur antenna will do, and the station's equipment can easily fit in a suitcase. Three skilled operators should be [__A_TAG_PLACEHOLDER_0__]provided, so the station can be “listening in” 24 hours a day.

The office should be provided with tables of frequency of the language of the enemy, covering single letters and digraphs; a dictionary and grammar of that language; copies of the War Department Code, Western Union Code and any other available ones; types of apparatus or, at least, data on apparatus and cipher methods in use by the enemy; and a safe filing cabinet and card index for filing messages examined. A typewriter is also desirable.

The office should have frequency tables of the enemy's language, including single letters and digraphs; a dictionary and grammar of that language; copies of the War Department Code, Western Union Code, and any other available ones; information on the types of equipment or at least data on the equipment and cipher methods used by the enemy; and a secure filing cabinet and card index for organizing examined messages. A typewriter is also recommended.

The office work on a cipher under examination should be done on paper of a standard and uniform size. Printed forms containing twenty-six ruled lines and a vertical alphabet are convenient and save time in preparation of frequency tables. Any new cipher methods which are found to be in use by the enemy should, when solved, be communicated to all similar offices in the Army for their information.

The office work on a cipher being examined should be done on paper of standard and uniform size. Printed forms with twenty-six ruled lines and a vertical alphabet are handy and save time when preparing frequency tables. Any new cipher methods discovered to be used by the enemy should, once solved, be communicated to all similar offices in the Army for their awareness.

Unless an enemy were exceedingly vigilant and changed keys and methods frequently, such an office would, in a few days, be in a position to disclose completely all intercepted cipher communications of the enemy with practically no delay. [4]

Unless an enemy was extremely alert and frequently changed their keys and methods, such an office would, in just a few days, be able to fully disclose all intercepted encrypted communications from the enemy with almost no delay. [__A_TAG_PLACEHOLDER_0__]

Chapter II

Principles of Mechanism of a Written Language

With a few exceptions, notably Chinese, all modern languages are constructed of words which in turn are formed from letters. In any given language the number of letters, and their conventional order is fixed. Thus English is written with 26 letters and their conventional order is A, B, C, D, E, etc. Some letters are used very frequently and others rarely. In fact, if ten thousand consecutive letters of a text be counted and the frequency of occurrence of each letter be noted, the numbers found will be practically identical with those obtained from any other text of ten thousand letters in the same language. The relative proportion of occurrence of the various letters will also hold approximately for even very short texts.

With a few exceptions, especially Chinese, all modern languages are made up of words that are formed from letters. In any language, the number of letters and their usual order is set. For example, English uses 26 letters, arranged in the order of A, B, C, D, E, and so on. Some letters appear very often while others are used less frequently. In fact, if you count ten thousand consecutive letters from a text and note how often each letter appears, the results will be almost the same as those from any other text of ten thousand letters in the same language. The relative frequency of different letters will also be roughly consistent, even for very short texts.

Such a count of a large number of letters, when it is put in the form of a table, is known as a frequency table. Every language has its own distinctive frequency table and, for any given language, the frequency table is almost as fixed as the alphabet. There are minor differences in frequency tables prepared from texts on special subjects. For example, if the text be newspaper matter, the frequency table will differ slightly from one prepared from military orders and will also differ slightly from one prepared from telegraph messages. But these differences are very slight as compared with the differences between the frequency tables of two different languages.

A count of a large number of letters, when organized in a table, is called a frequency table. Every language has its own unique frequency table, and for any specific language, the frequency table is almost as consistent as the alphabet. There are minor variations in frequency tables created from texts on specific subjects. For example, if the text is from newspapers, the frequency table will be slightly different from one made from military orders, and it will also differ a bit from one created from telegraph messages. However, these differences are very small compared to the differences between the frequency tables of two different languages.

Again there is a fixed ratio of occurrence of [5]every letter with every other for any language and this, put in table form, constitutes a table of frequency of digraphs. In the same way a table of trigraphs, showing the ratio of occurrence of any three letters in sequence, could be prepared, but such a table would be very extensive and a count of the more common three letter combinations is usually used.

Again, there is a fixed ratio of occurrence of [__A_TAG_PLACEHOLDER_0__] every letter with every other letter in any language. When arranged in a table, this becomes a frequency table of digraphs. Similarly, a table of trigraphs, which shows the occurrence ratio of any three letters in sequence, could be created; however, such a table would be very large, and a count of the more common three-letter combinations is typically used.

Other tables, such as frequency of initial and final letters of words, might be of value but the common practice is to put cipher text into groups of five or ten letters each and eliminate word forms. This is almost a necessity in telegraphic and radio communication to enable the receiving operator to check correct receipt of a message. He must get five letters, neither more nor less, per word or he is sure a mistake has been made. There is little difficulty, as a rule, in restoring word forms in the deciphered message.

Other tables, like the frequency of first and last letters of words, might be useful, but the usual practice is to break cipher text into groups of five or ten letters and remove word structures. This is almost essential in telegraphic and radio communication so that the operator receiving the message can verify that it was received correctly. They need to get five letters, no more and no less, for each word, or they'll know a mistake has happened. Generally, there’s not much trouble restoring word forms in the deciphered message.

We will now take up, in order, the various frequency tables and linguistic peculiarities of English and Spanish. Frequency tables for French, German, and Italian for single letters will follow. All frequency tables have been re-calculated from at least ten thousand letters of text and compared with existing tables. No marked difference has been found in any case between the re-calculated tables and those already in use.

We will now discuss, in order, the different frequency tables and unique features of English and Spanish. Frequency tables for French, German, and Italian for single letters will come next. All frequency tables have been recalculated from at least ten thousand letters of text and compared with existing tables. No significant differences have been found in any case between the recalculated tables and those currently in use.

Data for Solution of Ciphers in English

Table I.—Normal frequency table. Frequency for ten thousand letters and for two hundred letters. This latter is put in graphic form and is necessarily an approximation. Taken from military orders and reports, English text. [6]

Table 1.—Normal frequency table. Frequency for ten thousand letters and for two hundred letters. This latter is shown in graphic form and is necessarily an approximation. Taken from military orders and reports, English text. [__A_TAG_PLACEHOLDER_0__]

	10,000 Letters	200 Letters
A	778	16	1111111111111111
B	141	3	111
C	296	6	111111
D	402	8	11111111
E	1277	26	11111111111111111111111111
F	197	4	1111
G	174	3	111
H	595	12	111111111111
I	667	13	1111111111111
J	51	1	1
K	74	2	11
L	372	7	1111111
M	288	6	111111
N	686	14	11111111111111
O	807	16	1111111111111111
P	223	4	1111
Q	8
R	651	13	1111111111111
S	622	12	111111111111
T	855	17	11111111111111111
U	308	6	111111
V	112	2	11
W	176	3	111
X	27
Y	196	4	1111
Z	17

Vowels AEIOU = 38.37%; consonants LNRST = 31.86%; consonants JKQXZ = 1.77%.

The vowels may be safely taken as 40%, consonants LNRST as 30% and consonants JKQXZ as 2%.

The vowels can be considered as 40%, consonants LNRST as 30%, and consonants JKQXZ as 2%.

Order of letters: E T O A N I R S H D L U C M P F Y W G B V K J X Z Q.

Table II.—Frequency table for telegraph messages, English text. This table varies slightly from the standard frequency table because the common word “the” is rarely used in telegrams and there is a tendency to use longer and less common words in preparing telegraph messages. [7]

Table 2.—Frequency table for telegraph messages, English text. This table differs slightly from the standard frequency table because the common word “the” is rarely used in telegrams, and there’s a tendency to use longer and less common words when preparing telegraph messages. [__A_TAG_PLACEHOLDER_0__]

	10,000 Letters	200 Letters
A	813	16	1111111111111111
B	149	3	111
C	306	6	111111
D	417	8	11111111
E	1319	26	11111111111111111111111111
F	205	4	1111
G	201	4	1111
H	386	8	11111111
I	711	14	11111111111111
J	42	1	1
K	88	2	11
L	392	8	11111111
M	273	6	111111
N	718	14	11111111111111
O	844	17	11111111111111111
P	243	5	11111
Q	38	1	1
R	677	14	11111111111111
S	656	13	1111111111111
T	634	13	1111111111111
U	321	6	111111
V	136	3	111
W	166	3	111
X	51	1	1
Y	208	4	1111
Z	6

In this table the vowels AEIOU = 40.08%, consonants LNRST = 30.77% and consonants JKQXZ = 2.25%.

In this table, the vowels AEIOU make up 40.08%, consonants LNRST account for 30.77%, and consonants JKQXZ represent 2.25%.

Orders of letters: E O A N I R S T D L H U C M P Y F G W B V K X J Q Z.

Table III.—Table of frequency of digraphs, duals or pairs (English). This table was prepared from 20,000 letters, but the figures shown are on the basis of 2,000 letters. For this reason they are, to a certain extent, approximate; that is, merely because no figures are shown for certain combinations, we should not assume that such combinations never occur but rather that they are rare. The letters in the horizontal line at the top and bottom are the leading letters; those in the vertical columns at the sides are the following letters. Thus in two thousand letters we may expect to find AH once and HA twenty-six times. [8]

Table 3.—Table of frequency of digraphs, duals or pairs (English). This table was created from 20,000 letters, but the numbers shown are based on 2,000 letters. For this reason, they are somewhat approximate; that is, just because no numbers are shown for certain combinations doesn't mean such combinations never occur, but rather that they are uncommon. The letters in the horizontal line at the top and bottom are the leading letters; those in the vertical columns on the sides are the following letters. So, in two thousand letters, we might expect to find AH once and HA twenty-six times. [__A_TAG_PLACEHOLDER_0__]

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
A		1	7	10	22	3	2	26	4	2	2	7	8	11	2	9		13	12	9		2	4	1	12
B	5			1	2				1			1	1	1	2				2	1	3				1
C	6		1	1	14	2			11					11	3			2	3	1	1		1		1
D	6			12	30	1			2			4		30	1			4	1	1	1		1		3
E		11	14	16	12	2	6	33	10	2	6	18	14	12	1	7		36	11	12	2	16	5		1	1
F	3			2	8	2	1		2			2	1	3	25				3	1	1				1
G	4			1	3				2					11	2			3							1
H	1		11	2	4	1	4					1		2	1	1		2	10	50			3		2
I	2	1	4	12	6	5	1	12	1		5	9	8	12	1	3		12	13	22	2	3	6		1	1
J		1
K	1		1		2													2	1		1
L	14	6	2	1	6	1	1	1	6			9		3	6	3		3	2	3	5
M	7			3	13	2		2	3				4	1	10			4	1	1					2
N	38			3	25		2	1	31		3		2	2	39			4	3		11		2
O	1	1	12	4	8	8	3	12	18	2		4	7	8	3	7		13	15	22		2	6	1	5
P	2			1	8				1			2	4	2	3	2		1	8	1	4			3	1
Q					2									1	1				1
R	16	1	3	3	40	3	6	2	6			1	2	1	25	8		2	2	8	11				2
S	16	1		3	25	1	2		17		1	2	1	12	7	2		9	11	6	11		1		6
T	25	1	3	12	13	5	2	3	20			2	1	24	8	2		16	20	11	6		2	2	7
U	1	2	1	6	1	3	2	2		3		3	1		17	1	5	3	5	5				1
V	3	1			5				5						3			2			5				1
W	1			2	8		1	1				1	1	2	4				2	3					3
X	1				4				2						1						1
Y	3	2		2	4		1	1				8	1	2		1		3	1	7
Z	1								1					1
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z

Table IV.—Order of frequency of common pairs to be expected in a count of 2,000 letters of military or semi-military English text. (Based on a count of 20,000 letters).

Table IV.—Order of frequency of common pairs expected in a count of 2,000 letters of military or semi-military English text. (Based on a count of 20,000 letters).

TH	50	AT	25	ST	20
ER	40	EN	25	IO	18
ON	39	ES	25	LE	18
AN	38	OF	25	IS	17
RE	36	OR	25	OU	17
HE	33	NT	24	AR	16
IN	31	EA	22	AS	16
ED	30	TI	22	DE	16
ND	30	TO	22	RT	16
HA	26	IT	20	VE	16

Table V.—Table of recurrence of groups of three letters to be expected in a count of 10,000 letters of English text.

THE	89	TIO	33	EDT	27
AND	54	FOR	33	TIS	25
THA	47	NDE	31	OFT	23
ENT	39	HAS	28	STH	21
ION	36	NCE	27	MEN	20

[9]

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Table VI.—Table of frequency of occurrence of letters as initials and finals of English words. Based on a count of 4,000 words; this table gives the figures for an average 100 words and is necessarily an approximation, like Table III. English words are derived from so many sources that it is not impossible for any letter to occur as an initial or final of a word, although Q, X and Z are rare as initials and B, I, J, Q, V, X and Z are rare as finals.

Table 6.—Table showing how often letters appear at the beginning and end of English words. This is based on a count of 4,000 words; the table provides averages for 100 words and is necessarily an approximation, similar to Table III. English words come from a wide variety of sources, so it's possible for any letter to appear at the start or end of a word. However, Below is an updated version that maintains fidelity to the original message., X, and Z are uncommon as initials, while B, I, J, Q, V, X, and Z are uncommon as finals.

Letters	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
Initial	9	6	6	5	2	4	2	3	3	1	1	2	4	2	10	2	-	4	5	17	2	-	7	-	3	-
Final	1	-	-	10	17	6	4	2	-	-	1	6	1	9	4	1	-	8	9	11	1	-	1	-	8	-

It is practically impossible to find five consecutive letters in an English text without a vowel and we may expect from one to three with two as the general average. In any twenty letters we may expect to find from 6 to 9 vowels with 8 as an average. Among themselves the relative frequency of occurrence of each of the vowels, (including Y when a vowel) is as follows:

It’s nearly impossible to find five consecutive letters in an English text without a vowel, and we can typically expect between one to three, with two being the general average. In any group of twenty letters, we can expect to find six to nine vowels, with eight being the average. The relative frequency of each vowel's occurrence (including Y when it acts as a vowel) is as follows:

A,	19.5%	E,	32.0%	I,	16.7%
O,	20.2%	U,	8.0%	Y,	3.6%

The foregoing tables give all the essential facts about the mechanism of the English language from the standpoint of the solution of ciphers. The use to be made of these tables will be evident when the solution of different types of ciphers is taken up.

The tables above provide all the key details about how the English language works in relation to solving ciphers. The purpose of these tables will become clear when we start working on various types of cipher solutions.

Data for the Solution of Ciphers in Spanish

The Spanish language is written with the following alphabet:

The Spanish language uses the following alphabet:

A B C CH D E F G H I J L LL
M N Ñ O P Q R RR S T U V X Y Z

while the exact sense often depends upon the use of accents over the vowels. However, in cipher work it is exceedingly inconvenient to use the permanent digraphs, CH, LL and RR and they do not appear as such in any specimens of Spanish or Mexican cipher [10]examined. Accented vowels and Ñ are also not found and we may, in general, say that a cipher whose text is Spanish will be prepared with the following alphabet:

while the exact meaning often depends on the use of accents over the vowels. However, in code work, it is extremely inconvenient to use the permanent digraphs, CH, LL, and RR, and they do not appear as such in any examples of Spanish or Mexican code [__A_TAG_PLACEHOLDER_0__]examined. Accented vowels and Ñ are also absent, and we can generally say that a code whose text is Spanish will be created with the following alphabet:

A B C D E F G H I J L M N O P Q R S T U V X Y Z

and the receiver must supply the accents and the tilde over the N to conform to the general sense.

and the receiver must provide the accents and the tilde over the N to match the general meaning.

However, many Mexican cipher alphabets contain the letters K and W. This is particularly true of the ciphers in use by secret service agents who must be prepared to handle words like NEW YORK, WILSON and WASHINGTON. The letters K and W will, however, have a negligible frequency except in short messages where words like these occur more than once.

However, many Mexican cipher alphabets include the letters K and W. This is especially true for the ciphers used by secret service agents who need to be ready to work with words like NYC, WILSON, and WASHINGTON. The letters K and W will, however, appear very rarely, except in short messages where these words come up more than once.

In this connection, if a cipher contains Mexican geographical names like CHIHUAHUA, MEXICO, MUZQUIZ, the letters H, X and Z will have a somewhat exaggerated frequency.

In this context, if a code includes Mexican place names like CHIHUAHUA, MEXICO, MUZQUIZ, the letters H, X, and Z will appear with a slightly higher frequency.

In Spanish, the letter Q is always followed by U and the U is always followed by one of the other vowels, A, E, I or O. As QUE or QUI occurs not infrequently in Spanish text, particularly in telegraphic correspondence, it is well worth noting that, if a Q occurs in a transposition cipher, we must connect it with U and another vowel. The clue to several transposition ciphers has been found from this simple relation.

In Spanish, the letter Q is always followed by U, and U is always followed by one of the other vowels, A, E, I, or O. Since QUE or QUI appear quite often in Spanish text, especially in telegrams, it's important to note that if a Q shows up in a transposition cipher, we must link it with U and another vowel. This simple relationship has provided clues to several transposition ciphers.

Table VII.—Normal frequency table for military orders and reports, calculated on a basis of 10,000 letters of Spanish text. The graphic form is on a basis of 200 letters. [11]

Table 7.—Standard frequency table for military orders and reports, calculated based on 10,000 letters of Spanish text. The graphic form is based on 200 letters. [__A_TAG_PLACEHOLDER_0__]

	10,000 Letters	200 Letters
A	1352	27	111111111111111111111111111
B	102	2	11
C	474	9	111111111
D	524	10	1111111111
E	1402	28	1111111111111111111111111111
F	91	2	11
G	137	3	111
H	102	2	11
I	606	12	111111111111
J	41	1	1
L	517	10	1111111111
M	300	6	111111
N	619	12	111111111111
O	818	16	1111111111111111
P	257	5	11111
Q	87	2	11
R	751	15	111111111111111
S	724	14	11111111111111
T	422	8	11111111
U	387	7	1111111
V	85	2	11
X	6
Y	103	2	11
Z	42	1	1

In this table the vowels AEIOU = 45.65%; consonants LNRST = 30.33%; consonants JKQXZ = 1.76%.

In this table, the vowels AEIOU make up 45.65%; consonants LNRST account for 30.33%; and consonants JKQXZ represent 1.76%.

Order of letters:

Letter sequence:

E A O R S N I D L C T U M P G Y (BH) F Q V Z J X.

Table VIII.—Table of frequency of digraphs, duals or pairs, Spanish text. Like Table III, this table is on the basis of 2,000 letters although prepared from a count of 20,000 letters. For this reason it is, to a certain extent an approximation; that is, merely because no figures are shown for certain combinations, we should not assume that such combinations never occur but rather that they are rare. The letters in the horizontal lines at the top and bottom are the leading letters; those in the vertical columns at the sides are the following letters. Thus, in two thousand letters, we may expect to find AI twice and IA twenty-three times. [12]

Table 8.—Frequency table of digraphs, duals, or pairs in Spanish text. Like Table III, this table is based on 2,000 letters, although it was prepared from a count of 20,000 letters. For this reason, it is somewhat of an approximation; just because certain combinations aren’t shown, we shouldn’t assume they never happen, but rather that they are uncommon. The letters in the horizontal rows at the top and bottom are the leading letters; those in the vertical columns on the sides are the following letters. So, in two thousand letters, we might expect to find AI twice and IA twenty-three times. [__A_TAG_PLACEHOLDER_0__]

	A	B	C	D	E	F	G	H	I	J	L	M	N	O	P	Q	R	S	T	U	V	X	Y	Z
A	9	4	19	11	5		6	17	23		54	18	9	3	20		29	11	21	8	6		2	5	A
B	6								3			1		4											B
C	24		6	6	24				5		3		8	8			9	5		2			2		C
D	31				29				3				19	13			10	9					4		D
E	12	2	6	59	10		1	5	7	2	12	18	22	4	9		38	25	28	25	3		3		E
F	4				4						4		3					3					1		F
G	2				4				8				4											2	G
H	2		12		10													2					1		H
I	2		23	16		5	2				3	11	13				6	10	5		3				I
J	3				2								1												J
L	21	3	6		39	3	3		7		21		5	6			12	2		2					L
M	12				6				5		1		6	15			7	2		6			1		M
N	32				46		2		8					32						12			2		N
O			26	22	2	6	3	4	9		16	2	8		20		15	7	11						O
P	13				3				2		4	9	2	7			4	11							P
Q	11	5									1		2				3		1						Q
R	40				27	2			4		4			36	3		11		17	3					R
S	39				52				10				7	14			2			14			3		S
T	5				13				4		4		18	5			6	30							T
U	2		4	2	6	3	4			5		2	6		4	17		15	2				1		U
V	2				2						2			2				2					2		V
X																									X
Y	5				6									2				5		2				2	Y
Z	1				2								1				4			2					Z
	A	B	C	D	E	F	G	H	I	J	L	M	N	O	P	Q	R	S	T	U	V	X	Y	Z

Table IX.—Order of frequency of common pairs to be expected in a count of 2,000 letters of Spanish military orders and reports. Based on Table VIII.

Table 9.—Order of frequency of common pairs that you can expect in a count of 2,000 letters of Spanish military orders and reports. Based on Table VIII.

DE	59	ON	32	AC	24
LA	54	AD	31	EC	24
ES	52	ST	30	CI	23
EN	46	ED	29	IA	23
AR	40	RA	29	DO	22
AS	39	TE	28	NE	22
EL	39	ER	27	AL	21
RE	38	CO	26	LL	21
OR	36	SE	25	PA	20
AN	32	UE	25	PO	20

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Alphabetic Frequency Tables

(Truesdell)

Frequency of occurrence in 1,000 letters of text:

Letter	French	German	Italian	Portuguese
A	80	52	117	140
B	6	18	6	6
C	33	31	45	34
D	40	51	31	40
E	197	173	126	142
F	9	21	10	12
G	7	42	17	10
H	6	41	6	10
I	65	81	114	59
J	3	1	1	5
K	1	10	1
L	49	28	72	32
M	31	20	30	46
N	79	120	66	48
O	57	28	93	110
P	32	8	30	28
Q	12	1	3	16
R	74	69	64	64
S	66	57	49	88
T	65	60	60	43
U	62	51	29	46
V	21	9	20	15
W	1	15
X	3	1	1	1
Y	2	1	1	1
Z	1	14	12	4

Order of Frequency

French

German

German

Italian

Portuguese

Portuguese

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Graphic Frequency Tables

Frequency of occurrence in 200 letters of text.

Frequency of occurrence in 200 characters of text.

French

French

A	16	1111111111111111
B	2	11
C	6	111111
D	10	1111111111
E	39	111111111111111111111111111111111111111
F	2	11
G	1	1
H	1	1
I	13	1111111111111
J	1	1
K
L	10	1111111111
M	6	111111
N	16	1111111111111111
O	11	11111111111
P	6	111111
Q	2	11
R	15	111111111111111
S	13	1111111111111
T	13	1111111111111
U	12	111111111111
V	4	1111
W
X	1	1
Y
Z

Italian

Italian cuisine

A	23	11111111111111111111111
B	1	1
C	9	111111111
D	6	111111
E	25	1111111111111111111111111
F	2	11
G	3	111
H	1	1
I	23	11111111111111111111111
L	14	11111111111111
M	6	111111
N	13	1111111111111
O	19	1111111111111111111
P	6	111111
Q
R	13	1111111111111
S	10	1111111111
T	12	111111111111
U	6	111111
V	4	1111
X
Y
Z	2	11

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German

A	10	1111111111
B	4	1111
C	6	111111
D	10	1111111111
E	32	11111111111111111111111111111111
F	4	1111
G	8	11111111
H	8	11111111
I	16	1111111111111111
J
K	2	11
L	6	111111
M	4	1111
N	24	111111111111111111111111
O	6	111111
P	2	11
Q
R	14	11111111111111
S	11	11111111111
T	12	111111111111
U	10	1111111111
V	2	11
W	3	111
X
Y
Z	3	111

Portuguese

A	28	1111111111111111111111111111
B	1	1
C	7	1111111
D	8	11111111
E	28	1111111111111111111111111111
F	2	11
G	2	11
H	2	11
I	12	111111111111
J	1	1
L	6	111111
M	9	111111111
N	10	1111111111
O	22	1111111111111111111111
P	6	111111
Q	3	111
R	13	1111111111111
S	18	111111111111111111
T	9	111111111
U	9	111111111
V	3	111
X
Y
Z	1	1

[16]

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1 Occurrence rare, usually in proper names. ↑

1 Rarely happens, typically found in proper names. ↑

Chapter III

Technique of Cipher Examination

In time of active operations it is important that captured or intercepted cipher messages reach the examining office with the least possible delay. The text of messages, captured at a distance from the examining office, should be sent to the office by telegraph or telephone, the original messages being forwarded to the office as soon thereafter as possible.

In times of active operations, it's crucial that captured or intercepted cipher messages get to the examining office as quickly as possible. Messages captured far from the office should be sent via telegraph or telephone, with the original messages forwarded to the office as soon as possible afterward.

The preamble, “place from,” date, address and signature, give most important clues as to the language of the cipher, the cipher method probably used, and even the subject matter of the message. If the whole of a telegraphic or radio message is in cipher, it is highly probable that the preamble, “place from,” etc., are in an operators’ cipher and are distinct from the body of the message. As these operators’ ciphers are necessarily simple, an attempt should always be made to discover, by methods of analysis to be set forth later, the exact extent of the operator’s cipher and then to decipher the parts of the messages enciphered with it.

The preamble, "place from," date, address, and signature provide crucial hints about the language of the cipher, the likely cipher method used, and even the topic of the message. If the entire telegraphic or radio message is in cipher, it's very likely that the preamble, "place from," etc., are in an operators' cipher and are separate from the main message. Since these operators' ciphers are usually straightforward, one should always try to determine, using analysis methods to be discussed later, the precise extent of the operator's cipher and then decode the sections of the messages that are encoded with it.

In military messages, we almost invariably find the language of the text to be that of the nation to which the military force belongs. The language of the text of the message of secret agents is, however, another matter and, in dealing with such messages, we should use all available evidence, both external and internal, before deciding finally on the language used. Whenever a frequency table can be prepared, [17]such a table will give the best evidence for this purpose.

In military communications, we usually see the language of the message reflecting that of the nation to which the military force is affiliated. However, the language used in messages from secret agents is different, and when handling these messages, we should consider all available evidence, both external and internal, before making a final decision on the language used. Whenever a frequency table can be created, [__A_TAG_PLACEHOLDER_0__] that table will provide the most reliable evidence for this purpose.

All work in enciphering and deciphering messages and in copying ciphers should be done with capital letters. There is much less chance of error when working with capitals and, with little practice, it is just about as fast. An additional safeguard is to use black ink or pencil for the plain text and colored ink or pencil for the cipher. A separate color may be used for the key when necessary.

All work in encoding and decoding messages and in copying codes should be done using capital letters. There's much less chance of making a mistake when working with capitals, and with a bit of practice, it's nearly as quick. An extra precaution is to use black ink or pencil for the plain text and colored ink or pencil for the code. A different color can be used for the key when needed.

The following blank form is suggested as convenient for keeping a record of a cipher under examination. It should accompany the cipher through the examining process and should be filled in as the facts are determined. This record, the original cipher and all notes of work done during the examination, should be filed together when the examination is completed, whether the cipher has been solved or not. It may be that other ciphers solved later will give clues to the solution of such unsolved ciphers.

The following blank form is recommended for keeping track of a cipher being analyzed. It should be used throughout the examination process and filled out as the facts are established. This record, along with the original cipher and all notes from the examination, should be stored together once the examination is complete, regardless of whether the cipher has been solved. Later solved ciphers may provide hints for solving those that remain unsolved.

The first column of this blank should be filled out from data furnished by the officer obtaining the cipher from the enemy. A general order, emphasizing the importance of promptly forwarding captured or intercepted ciphers to an examining office, could specify that a brief report embodying this data should be forwarded with each cipher.

The first column of this blank should be filled out with information provided by the officer who got the cipher from the enemy. A general order, highlighting the importance of quickly sending captured or intercepted ciphers to a review office, could specify that a brief report containing this information should be sent with each cipher.

The second column of the blank should be filled out progressively as the work proceeds. The office number should be a serial one, the first cipher examined being No. 1. The date and hour of receipt at examining office will be a check as to the time required to transmit it from place of capture. The spaces “From,” “At,” “To,” “At,” “Date,” are for [18]the information concerning sender and addressee of the cipher and are to be obtained from the message. In case an operators’ cipher has been used, these parts of the message will have to be deciphered before the blanks can be filled in.

The second column of the blank should be filled out progressively as the work continues. The office number should be sequential, starting with No. 1 for the first cipher examined. The date and time of receipt at the examining office will serve as a check for the time it took to transmit it from the location of capture. The spaces "From,", "At," "To," "At," and "Date" are for [__A_TAG_PLACEHOLDER_0__] information about the sender and recipient of the cipher and should be obtained from the message. If an operator's cipher has been used, these parts of the message will need to be deciphered before the blanks can be filled in.

Intelligence Section, General Staff

1st Field Army

	-----------	-----------
	Place,	Date

Record of Cipher Examination

This cipher obtained by
-----------
-----------
at	-----------	-----------
on	-----------	-----------
	(date)	(hour)

How being transmitted when obtained. (Underscore means used and enter data on sending and receiving stations).

How it's transmitted when obtained. (Underscore indicates used and enter data on sending and receiving stations).

Sending Station

Receiving Station

Radio

Telephone

Telegraph

Buzzer

Helio

Lantern

Flag

Cyclist

from

Foot Messenger

from

Mtd. Messenger

from

How obtained. (Underscore means used). Captured before delivery to addressee. Captured after delivery to addressee. Intercepted, not received by addressee. Copied, but received by addressee.

How obtained. (Underscore means used). Captured before delivery to the recipient. Captured after delivery to the recipient. Intercepted, not received by the recipient. Copied, but received by the recipient.

Remarks:

Comments:

Office Number. Understood. Please provide the text you would like me to modernize.

Received	-----------	-----------
	(Date)	(Hour)

From Understood. Please provide the text for me to modernize.

At Understood! Please provide the text for modernization.

To Understood! Please provide the text you'd like me to modernize.

At Understood! Please provide the text you would like me to modernize.

Date Understood! Please provide the text for modernization.

Probable language of text Understood! Please provide the text you'd like me to modernize.

Class		Transposition Please provide the text to be modernized.
		-----------
		Replacement Understood. Please provide the text you'd like me to modernize.
		-----------

Case I'm ready for the text you would like me to modernize. Please provide it.

Remarks:

Solution completed	---------	----------
	(date)	(hour)

Language of text I'm ready for your text! Please provide the short phrases you'd like me to modernize.

Key, (if known) Sure! Please provide the text you would like me to modernize.

-----------

Type Understood! Please provide the text you'd like me to modernize.

File No. Understood! Please provide the text you’d like me to modernize.

-----------

Examiner.

The probable language of the text is assumed from the preceding data and, if necessary, from [19]internal evidence. Thus a cipher from a Mexican source and not containing K or W is probably in Spanish.

The likely language of the text is inferred from the previous data and, if needed, from [__A_TAG_PLACEHOLDER_0__]internal evidence. Therefore, a cipher from a Mexican source that does not include K or W is probably in Spanish.

The class and case are determined by the rules laid down later. The space for remarks is to permit notation of any special features. When the solution is completed, the date and hour are noted, the language of text and key (if determined) are entered and a type number, to identify it with other ciphers prepared by the same method (but not necessarily the same key), is given to it. The file number is for convenience in filing and in preparation of a card index.

The class and case are determined by the rules set out later. The remarks section is there to note any special features. When the solution is finished, the date and time are recorded, the language of the text and key (if decided) are entered, and a type number is assigned to identify it with other ciphers created using the same method (but not necessarily the same key). The file number is for ease of filing and for creating a card index.

The process of examination in an office with one examiner, one stenographer and one clerk, might be as follows: On receipt of a captured cipher with accompanying report, the stenographer makes four copies of the cipher on the typewriter. The clerk and stenographer then check the work. The stenographer then proceeds to fill out the first column and first two lines of the second column of the record blank from the report of the capturing officer, keeping the original cipher and two copies with the record. He may also fill out the first seven lines of the second column, if this data is on the captured cipher in plain text. In the meantime the clerk is counting and setting down the whole number of letters of the cipher and the occurrence of AEIOU, LNRST, and JKQXZ, while the examining officer is looking over the cipher for possible recurring groups of letters and underlining them when found.

The examination process in an office with one examiner, one stenographer, and one clerk might go like this: When a captured cipher and its report are received, the stenographer makes four copies of the cipher using a typewriter. The clerk and stenographer then check the work. The stenographer fills out the first column and the first two lines of the second column of the record sheet using the report from the capturing officer, keeping the original cipher and two copies with the record. He may also fill out the first seven lines of the second column if that information is available in plain text on the captured cipher. Meanwhile, the clerk counts and records the total number of letters in the cipher and the occurrences of AEIOU, LNRST, and JKQXZ, while the examining officer reviews the cipher for possible recurring letter groups and underlines them when identified.

This work being completed, the examining officer is in a position, ordinarily, to decide on the class of the cipher and he may have found something in his examination which will lead him to the case under the class. The clerk in this preliminary count should [20]keep track of the total occurrence of each of the fifteen check letters and not of the three groups given above. This takes a little longer but when done, the data for fifteen letters of the alphabet for a frequency table is completed, leaving only eleven other letters, and in Spanish, but nine, to be counted, in case it is necessary to prepare a frequency table.

Once this work is finished, the examining officer is usually able to determine the type of cipher and may have discovered something during his review that guides him to the relevant case under that type. The clerk in this initial count should [__A_TAG_PLACEHOLDER_0__]keep track of how often each of the fifteen check letters appears, rather than focusing on the three groups mentioned earlier. This takes a bit more time, but once completed, the data for the fifteen letters of the alphabet for a frequency table will be ready, leaving only eleven other letters to be counted, or nine in the case of Spanish, should there be a need to prepare a frequency table.

If the examining officer decides the cipher to be of the transposition class, no further work with frequency tables is necessary. The clerk should proceed to count and set down the number of vowels in each line and column and the examining officer should look for any occurrence of the letter Q and try to connect it with U and another vowel. The stenographer may be set to work putting the cipher into rectangles of different dimensions. The clerk’s work gives data for possible rearrangement, for if the vowels are much out of proportion at any point, they must be connected with the proper proportion of consonants as a first step in rearrangement. Work with transposition ciphers must necessarily include much of the fit and try method. The details of this work are taken up later.

If the examining officer determines that the cipher is a transposition type, no further analysis with frequency tables is needed. The clerk should count and record the number of vowels in each row and column, while the examining officer should look for any instance of the letter Q and try to link it with U and another vowel. The stenographer can start organizing the cipher into rectangles of various sizes. The clerk’s findings provide data for potential rearrangement because if the vowels are significantly out of balance at any point, they need to be paired with the right amount of consonants as a first step in rearranging. Working with transposition ciphers will often involve a lot of trial and error. The specifics of this work will be discussed later.

If a cipher seems to be a substitution cipher, the examining officer should look over the frequency of occurrence of each of the fifteen letters counted. If some letters (it is of no importance at present which ones) occur much more frequently than others and some occur rarely or not at all, we may safely decide on Case 4, 5 or 6 and let the clerk proceed to finish the frequency table for the message. On the other hand, if all the fifteen letters examined occur with somewhere near the same frequency—for example, the most common letter occurring not over three or four times as often as the least common letter—we may at once eliminate the first three cases [21]and let the clerk proceed to examine the cipher for recurring pairs and groups, counting the intervening letters, so that the examining officer may decide whether Case 7, or some more complicated case, should be chosen.

If a cipher looks like a substitution cipher, the examining officer should check the frequency of each of the fifteen letters counted. If some letters (it doesn't matter which ones for now) appear much more often than others while some are rare or not present at all, we can confidently focus on Case 4, 5, or 6 and let the clerk finish the frequency table for the message. However, if all fifteen letters show up with roughly the same frequency—for instance, the most common letter appears no more than three or four times as often as the least common letter—we can immediately rule out the first three cases [__A_TAG_PLACEHOLDER_0__] and allow the clerk to look for recurring pairs and groups, counting the letters in between, so that the examining officer can determine whether to choose Case 7 or some more complex case.

If something more complicated than Case 7 has been used and other ciphers are on hand awaiting examination, the cipher should go into the unsolved file to be worked on when other work permits, unless the contents of the cipher are believed to be very important. Every opportunity should be taken to clean up the unsolved file and, whenever a message is solved, the methods should be tried, if applicable, to everything remaining in the file.

If something more complex than Case 7 has been used and other ciphers are available for review, the cipher should go into the unsolved file to be addressed when time allows, unless the contents of the cipher are thought to be very important. Every chance should be taken to tidy up the unsolved file, and whenever a message is solved, the methods should be applied, if relevant, to everything still in the file.

The first few days or weeks after the establishment of an examining office will be the most trying time. When solved ciphers begin to pile up, the methods of the enemy will be more and more apparent and it will often be possible to determine the method from knowledge of the name of the sender and receiver.

The first few days or weeks after setting up an examining office will be the toughest period. As solved ciphers start to accumulate, the enemy's methods will become clearer, and it will often be possible to figure out their approach just by knowing the names of the sender and receiver.

When a cipher has been solved, the solution should be prepared in triplicate and given the serial number of the cipher. Any parts which are not clear, through errors in enciphering or in transmission, should be underlined or otherwise made conspicuous, so that the head of the Intelligence Section may note them and, possibly, from other sources, supply the deficiency.

When a cipher has been solved, the solution should be prepared in three copies and assigned the serial number of the cipher. Any unclear parts, due to mistakes in encoding or during transmission, should be highlighted or marked in some way, so the head of the Intelligence Section can take note of them and possibly fill in the gaps from other sources.

One of the copies of the cipher and report of examination, with a copy of the solution, should be turned over at once to the head of the Intelligence Section or to the Chief of Staff. The other copies of the solution should be filed with the original cipher, the report of examination, and all work done on the cipher. [22]

One copy of the cipher and the examination report, along with a copy of the solution, should be handed over immediately to the head of the Intelligence Section or the Chief of Staff. The other copies of the solution should be filed with the original cipher, the examination report, and all related work on the cipher. [__A_TAG_PLACEHOLDER_0__]

Periodically, say once a week or even daily at the beginning of active operations, there should be an interchange between all examining offices of solved messages involving new methods used by the enemy. All the examining offices will thus be kept in touch. It may also be possible to assign certain hostile radio stations to each examining office to prevent duplication of work. [23]

Periodically, such as once a week or even daily at the start of active operations, there should be a sharing of solved messages between all examining offices that involve new methods used by the enemy. This way, all the examining offices will stay connected. It might also be possible to assign specific hostile radio stations to each examining office to avoid duplication of work. [__A_TAG_PLACEHOLDER_0__]

Chapter IV

Classes of Ciphers

There are, in general, two classes of ciphers. These are the transposition cipher and the substitution cipher.

There are generally two types of ciphers. These are the transposition cipher and the substitution cipher.

Substitution ciphers may be made up of substituted letters, numerals, conventional signs or combinations of all three; and furthermore, for a single letter of the original text there may be substituted a single letter, numeral or sign or two or more of each, or a whole word or group of figures, combination of conventional signs, or combinations of all three of these elements. Thus substitution ciphers may vary from those of extreme simplicity to those whose complication defies any ordinary method of analysis and whose solution requires the possession of long messages and much time and study. Fortunately the more difficult substitution ciphers are rarely used for military purposes, on account of the time and care required for enciphering and deciphering.

Substitution ciphers can consist of replaced letters, numbers, symbols, or a mix of all three. Furthermore, for each letter in the original text, you can substitute one letter, number, or symbol, or even two or more of each, or an entire word, a group of numbers, a mix of symbols, or combinations of all three elements. Therefore, substitution ciphers can range from very simple to extremely complex ones that are difficult to analyze and require lengthy messages, along with significant time and effort to solve. Luckily, the more challenging substitution ciphers are seldom used for military purposes because of the time and attention needed for encoding and decoding.

Transposition ciphers are limited to the characters of the original text. These characters are rearranged singly, according to some predetermined method or key (monoliteral transposition), or whole words are similarly rearranged (route cipher).

Transposition ciphers are restricted to the original text's characters. These characters are rearranged one-by-one, following a specific method or key (monoliteral transposition), or entire words are rearranged in a similar way (route cipher).

There may also be a combination of transposition and substitution methods in enciphering a message but in this case it will fall into the substitution class on first determination and after solution as a substitution cipher it must be handled as a transposition cipher. Examples of this case will be given. [24]

There might also be a mix of transposition and substitution methods used to encrypt a message. However, in this situation, it will initially be classified as a substitution cipher. Once solved, it should be treated as a transposition cipher. Examples of this scenario will be provided. [__A_TAG_PLACEHOLDER_0__]

We may also find transposition or substitution methods applied to words taken from a code book, or to numbers which represent these words. Thus cipher methods blend into code work, for a code is, after all, only a specialized substitution cipher.

We might also see transposition or substitution methods used for words from a codebook, or for numbers that represent those words. As a result, cipher methods mix with code work, since a code is basically just a specific type of substitution cipher.

We can now lay down the rules for determining whether any given cipher belongs to the substitution class or to the transposition class.

We can now establish the rules to determine whether any given cipher falls into the substitution class or the transposition class.

Count the number of letters in the message, the number of vowels, AEIOU, the number of the consonants, LNRST, and the number of the consonants, JKQXZ.

Count the number of letters in the message, the number of vowels, AEIOU, the number of consonants, LNRST, and the number of consonants, JKQXZ.

If the text is English and the cipher is a transposition cipher, this proportion will hold; vowels AEIOU constitute 40% of the whole; consonants LNRST, 30% and consonants JKQXZ, 3%.

If the text is in English and the cipher is a transposition cipher, this ratio will apply; vowels AEIOU make up 40% of the total; consonants LNRST, 30%, and consonants JKQXZ, 3%.

If the text be Spanish the proportions for a transposition cipher will be: vowels AEIOU 45%, consonants LNRST, 30%; consonants JKQXZ, 2%.

If the text is Spanish, the proportions for a transposition cipher will be: vowels AEIOU 45%, consonants LNRST 30%; consonants JKQXZ 2%.

If these proportions do not hold within 5%, one way or the other, the cipher is certainly a substitution cipher. Note, however, that often the end of a message is filled with letters like K, X, Z to complete cipher words and it is best to neglect the last word or words in making a count. Also, if the cipher be a long one, this determination can safely be made by taking 100 or 200 consecutive letters of the message, either from the beginning or, if nulls at the beginning are suspected, from the interior of the message.

If these proportions are off by more than 5%, then the cipher is definitely a substitution cipher. Keep in mind, though, that the end of a message often has letters like K, X, Z to fill out cipher words, so it’s best to ignore the last word or words when counting. Additionally, if the cipher is long, you can reliably determine this by taking 100 or 200 consecutive letters from the message, either from the start or, if you suspect nulls at the beginning, from the middle of the message.

The distinction between the route cipher (transposition) and the substitution cipher where whole words are substituted for letters of the original text, must be made on the basis of the words actually used. It is better to consider such a message as a route cipher when the words used appear to have some consecutive meaning bearing on the situation [25]at hand. A substitution cipher of this variety would only be used for transmission of a short message of great importance and secrecy, and then the chances are that certain words corresponding to A, E, N, O and T would appear with such frequency as to point at once to the fact that a substitution cipher was used. Watch the initial or terminal letters in such a cipher; they may spell the message.

The difference between the route cipher (transposition) and the substitution cipher, where entire words are replaced with letters from the original text, should be based on the actual words used. It’s more useful to view such a message as a route cipher when the chosen words seem to imply some continuous meaning related to the situation [__A_TAG_PLACEHOLDER_0__] at hand. A substitution cipher like this would typically be employed for sending a crucial and highly confidential short message, and in that case, it’s likely that certain words related to A, E, N, O, and T would appear often enough to reveal that a substitution cipher was used. Pay attention to the first or last letters in such a cipher; they might form the message.

In general, the determination of class by proportion of vowels, common consonants and rare consonants may be safely followed. We will now proceed to the examination of the more common varieties of each class of cipher. [26]

In general, you can safely classify based on the ratio of vowels, common consonants, and rare consonants. Now, let's move on to examining the more common types of each cipher class. [__A_TAG_PLACEHOLDER_0__]

Chapter V

Examination of Transposition Ciphers

After having decided that a cipher belongs to the transposition class, it remains to decide on the variety of cipher used. As, by definition, a transposition cipher consists wholly of characters of the original message, rearranged according to some law, we may, in general, say that such a cipher offers fewer difficulties in solution than a substitution cipher. A transposition cipher is like a picture puzzle; the parts are all there and the solution merely involves their correct arrangement.

After deciding that a cipher is a transposition type, the next step is to determine the specific kind of cipher used. By definition, a transposition cipher consists entirely of the original message's characters, rearranged according to specific rules. Generally, we can say that this type of cipher is easier to solve than a substitution cipher. A transposition cipher is similar to a jigsaw puzzle; all the pieces are present, and the solution simply requires them to be arranged correctly.

Case 1.—Geometrical ciphers. This case includes all ciphers in which a certain number of the characters are chosen so that they will form a square or rectangle of predetermined dimensions; and then these characters are arranged according to a geometrical design.

Case 1.—Geometrical ciphers. This case includes all ciphers where a specific number of characters are selected to create a square or rectangle of set dimensions; then these characters are organized based on a geometric pattern.

Taking the message:

A B C D E F G H I J K L M N O P Q R S T U V W X

of twenty-four letters and assuming a rectangle of six letters horizontally, and four letters vertically, we may have:

of twenty-four letters and assuming a rectangle of six letters horizontally and four letters vertically, we may have:

(a) Simple Horizontal:

Simple Horizontal

A B C D E F	F E D C B A	S T U V W X	X W V U T S
G H I J K L	L K J I H G	M N O P Q R	R Q P O N M
M N O P Q R	R Q P O N M	G H I J K L	L K J I H G
S T U V W X	X W V U T S	A B C D E F	F E D C B A

(b) Simple Vertical:

Simple Vertical

A E I M Q U	D H L P T X	U Q M I E A	X T P L H D
B F J N R V	C G K O S W	V R N J F B	W S O K G C
C G K O S W	B F J N R V	W S O K G C	V R N J F B
D H L P T X	A E I M Q U	X T P L H D	U Q M I E A

[27]

[__A_TAG_PLACEHOLDER_0__]

A B C D E F	F E D C B A	X W V U T S	S T U V W X
L K J I H G	G H I J K L	M N O P Q R	R Q P O N M
M N O P Q R	R Q P O N M	L K J I H G	G H I J K L
X W V U T S	S T U V W X	A B C D E F	F E D C B A

(d) Alternate Vertical:

Alternate Vertical

A H I P Q X	D E L M T U	X Q P I H A	U T M L E D
B G J O R W	C F K N S V	W R O J G B	V S N K F C
C F K N S V	B G J O R W	V S N K F C	W R O J G B
D E L M T U	A H I P Q X	U T M L E D	X Q P I H A

(e) Simple Diagonal:

Simple Diagonal

A B D G K O	G K O S V X	O K G D B A	X V S O K G
C E H L P S	D H L P T W	S P L H E C	W T P L H D
F I M Q T V	B E I M Q U	V T Q M I F	U Q M I E B
J N R U W X	A C F J N R	X W U R N J	R N J F C A

A C F J N R	J N R U W X	R N J F C A	X W U R N J
B E I M Q U	F I M Q T V	U Q M I E B	V T Q M I F
D H L P T W	C E H L P S	W T P L H D	S P L H E C
G K O S V X	A B D G K O	X V S O K G	O K G D B A

(f) Alternate Diagonal:

A B F G N O	G N O U V X	O N G F B A	X V U O N G
C E H M P U	F H M P T W	U P M H E C	W T P M H F
D I L Q T V	B E I L Q S	V T Q L I D	S Q L I E B
J K R S W X	A C D J K R	X W S R K J	R K J D C A

A C D J K R	J K R S W X	R K J D C A	X W S R K J
B E I L Q S	D I L Q T V	S Q L I E B	V T Q L I D
F H M P T W	C E H M P U	W T P M H F	U P M H E C
G N O U V X	A B F G N O	X V U O N G	O N G F B A

(g) Spiral, clockwise:

Spiral clockwise

A B C D E F	L M N O P A	I J K L M N	D E F G H I
P Q R S T G	K V W X Q B	H U V W X O	C R S T U J
O X W V U H	J U T S R C	G T S R Q P	B Q X W V K
N M L K J I	I H G F E D	F E D C B A	A P O N M L

(h) Spiral, counter clockwise:

Spiral, counterclockwise:

A P O N M L	N M L K J I	I H G F E D	F E D C B A
B Q X W V K	O X W V U H	J U T S R C	G T S R Q P
C R S T U J	P Q R S T G	K V W X Q B	H U V W X O
D E F G H I	A B C D E F	L M N O P A	I J K L M N

It is simply a matter of inspection to read a message in a cipher of this type, once the dimensions of the rectangles have been determined. We place the whole or a portion of the message in such rectangles and read horizontally, vertically and diagonally forward and backward. Parts of words will at once be apparent and the whole message is soon deciphered. Two examples will show the process. [28]

It's just a matter of checking things out to read a message in this kind of code, once you know the size of the rectangles. We put the entire message or part of it into these rectangles and read it horizontally, vertically, and diagonally in both directions. You'll quickly notice parts of words, and soon the whole message is decoded. Two examples will demonstrate the process. [__A_TAG_PLACEHOLDER_0__]

Message

Message

ILVGIOIAEITSRNMANHMNG

This message contains eight vowels or 38% out of twenty-one letters, and the letters LNRST occur 7 times or 33%, the letters XQJKZ not appearing. It is therefore a transposition cipher. Twenty-one letters immediately suggest seven columns of three letters each or three columns of seven letters each. Trying the former we have:

This message has eight vowels, which is 38% of the twenty-one letters, and the letters LNRST appear 7 times, making up 33%. The letters XQJKZ do not show up at all. So, this is a transposition cipher. The twenty-one letters hint at either seven columns of three letters each or three columns of seven letters each. If we try the first option, we have:

I L V G I O I

A E I T S R N

M A N H M N G

and reading down each column in succession (Case 1-b) reveals the message to be “I am leaving this morning.”

and reading down each column in order (Case 1-b) reveals the message to be “I am leaving this morning.”

Message

Message

M S I B R	O R S E E	V U E E M	C O R E R	E L I D E	T O E P Q
E N R E R	N S E R Y	E C O L L	E R E U S	P L U R C	E L O A J
A E H U H	P F A S O	N N O A A	E P I U A	P P E A C	U Q A R U
O P O E I	I R R M I	A F D A A	R Q U B O	Z A E G E	R S F S X

There are 120 letters in this message with 57 vowels or 47% vowels, and the letters LNRST occur 31 times or 26% of the whole.

There are 120 letters in this message with 57 vowels or 47% vowels, and the letters LNRST occur 31 times or 26% of the total.

Non-occurrence of K and W and vowel proportion leads us to the assumption that it is a transposition cipher of a Spanish text. The factors of 120 are 5 × 3 × 2 × 2 × 2. We may then have one rectangle of 4 × 30 or one of 5 × 24 or two of 5 × 12, or three of 5 × 8, or four of 5 × 6, or five of 3 × 8, or ten of 3 × 4, or twenty of 3 × 2. The message being in a rectangle of 4 × 30, we can inspect it as it stands and this is clearly not the arrangement if it be a geometrical transposition cipher at all. It is best however to try the largest possible rectangles first so we will put it in the form 5 × 24, thus:

Non-occurrence of K and W and the ratio of vowels leads us to believe that it is a transposition cipher of a Spanish text. The factors of 120 are 5 × 3 × 2 × 2 × 2. We could have one rectangle of 4 × 30 or one of 5 × 24, or two of 5 × 12, or three of 5 × 8, or four of 5 × 6, or five of 3 × 8, or ten of 3 × 4, or twenty of 3 × 2. With the message arranged in a rectangle of 4 × 30, we can examine it as is, and this is clearly not the layout if it is a geometrical transposition cipher at all. However, it’s best to try the largest possible rectangles first, so we will format it as 5 × 24, like this:

[29]

[__A_TAG_PLACEHOLDER_0__]

Here an inspection shows this to be Case 1-f, alternate diagonal, and the text to be “ME SITUO SOBRE PARRAL PORQUE ME PRESENCIA FUE REVELADA POR U”; here the sense breaks but note that U is the twelfth letter of the line and continue as if the rectangle were 5 × 12 and we have “NA PAREJA QU.” Now inspect the second rectangle of 5 × 12 in the same way and the sense continues “E SE ME ACERCO Y HUBO QUE RECHAZAR POR EL FUEGO ALLI ESRERO ORDENES FINISX”.

Here an inspection shows this to be Case 1-f, alternate diagonal, and the text to be “I POSITION MYSELF ON PARRAL BECAUSE MY PRESENCE WAS REVEALED BY U”; here the meaning breaks but note that U is the twelfth letter of the line and continue as if the rectangle were 5 × 12 and we have “ON THE COUPLE QU.” Now inspect the second rectangle of 5 × 12 in the same way and the meaning continues “If I come close and it needs to be rejected because of the fire there, I will give the order for FINISX..”

The practical way of examining a cipher of this type is to have several men prepare rectangles of different dimensions, using the letters of the cipher in the order received. The rectangles can be inspected very rapidly when once prepared. Note that the dimensions of any rectangle will rarely be such as to contain more than fifty letters, on account of the necessity of filling up a rectangle with nulls if the number of letters of the message is just a little greater than a multiple of the rectangle. Also large rectangles give, for all but the diagonal method, whole words in a line or column and these are easily noted.

The best way to analyze a cipher like this is to have several people create rectangles of different sizes using the letters of the cipher in the order they were received. Once these rectangles are prepared, they can be reviewed quickly. Keep in mind that the size of any rectangle will usually not exceed fifty letters, because you need to fill up a rectangle with placeholders if the number of letters in the message is just slightly more than a multiple of the rectangle. Also, large rectangles tend to display entire words in a row or column, except for the diagonal method, making them easy to spot.

The following ciphers come under Case 1:

The ciphers listed below fall under Case 1:

Case 1-i.—The rail fence cipher, useful as an operators’ cipher but permits of no variation and is therefore read almost as easily as straight text when the method is known. The message:

Case 1-i.—The rail fence cipher is useful for operators, but it allows for no variation and can therefore be read almost as easily as plain text once the method is known. The message:

HOSTILE CAVALRY HAS RETIRED

HOSTILE CAVALRY HAS WITHDRAWN

is written:

O T L C V L Y A R T R D

H S I E A A R H S E I E

and is sent:

OTLCV LYART RDHSI EAARH SEIEX [30]

OTLCV LYART RDHSI EAARH SEIEX [__A_TAG_PLACEHOLDER_0__]

Case 1-j.

Message

S S O H S	T P F O R	I E E A E
T Q N E T	F A I X E	G L F D R
A U L R N	O S R X L	H A T R O

To solve this cipher, read down the columns in this order 8, 1, 15, 2, 14, 3, 13, 4, 12, etc. A variation is to arrange the cipher so the columns are read upwards. Another is to arrange the ciphers so the columns are read alternately upward and downward. The factors of the number of letters in this case give the shape of the rectangle as usual.

To decode this cipher, read down the columns in this order: 8, 1, 15, 2, 14, 3, 13, 4, 12, and so on. One variation is to arrange the cipher so the columns are read upwards. Another option is to set up the ciphers so the columns are read alternately upward and downward. The factors of the total number of letters in this case determine the shape of the rectangle as usual.

It will be seen that there are a great number of possible transposition ciphers that come under Case 1 but practically all of them are useless from a military standpoint because they do not depend on a key which can be readily and frequently changed. However such ciphers constantly crop up in cipher examination, being used for special communication between parties who consider the regular military ciphers too complicated. Thus some of these expedients have been used.

It will be clear that there are many possible transposition ciphers that fall under Case 1, but nearly all of them are not useful from a military perspective because they do not rely on a key that can be easily and frequently changed. However, such ciphers frequently appear in cipher analysis, as they are used for special communication between parties who find the standard military ciphers too complex. As a result, some of these methods have been utilized.

Reversed Writing.—(Special case of Case 1-a).

Reversed Writing.—(Special case of Case __A_TAG_PLACEHOLDER_0__).

LEAVING TONIGHT is enciphered THGINOT GNIVAEL or it may be reversed by words, thus GNIVAEL THGINOT or by groups of five letters, thus IVAEL NOTGN XTHGI.

Leaving tonight is encoded as LEAVING TONIGHT or it can be reversed by words, thus EVIL NIGHTING or in groups of five letters, thus IVAEL NOTGN NIGHT.

Vertical Writing.—(Special case of Case 1-b). Same message is enciphered,

Vertical Text.—(Special case of Case 1-b). The same message is encoded,

LT
EO
AN
VI	and is sent, LTEOA NVIIG NHGTX.
IG
NH
GT

[31]

[__A_TAG_PLACEHOLDER_0__]

Case 2.—This case includes all transposition ciphers in which lines and columns of the text are rearranged according to some key word or key number. There are many varieties of this case but their solution usually is arrived at through the methods suggested for Case 1, that is, arrangement into appropriate rectangles and examination of lines and columns for words or syllables. Rearrangement of columns or lines follows until the solution is completed.

Case 2.—This case includes all transposition ciphers where the lines and columns of the text are rearranged based on a specific keyword or number. There are many different types of this case, but usually, the solution is found using the methods suggested for Case 1, which means organizing the text into suitable rectangles and checking the lines and columns for words or syllables. Columns or lines are rearranged until the solution is reached.

Case 2-a.

Message

HIIGF	TNGHI	NTCVN	IEIOT	CYIFY	LHAEA	ESNBA	EEEEN
RWGBN	YDELR	OAESG	RNEBO	VNLDA	ICAOA	LCNDT	IRGVA
CDOIE	SEREC	DVPEI	AFIFL	RINEH	ETT

There are 108 letters in this message and examination shows it to be a transposition cipher, English text. The number of letters, 108, immediately suggests a rectangle of 12 × 9 or 9 × 12 letters. Put into this form we have:

There are 108 letters in this message, and an analysis reveals that it’s a transposition cipher in English. The total of 108 letters hints at a rectangle of 12 × 9 or 9 × 12 letters. When arranged this way, we have:

	Vowels
H I I G F T N G H I N T	3
C V N I E I O T C Y I F	5
Y L H A E A E S N B A E	6
E E E N R W G B N Y D E	4
L R O A E S G R N E B O	5
V N L D A I C A O A L C	5
N D T I R G V A C D O I	4
E S E R E C D V P E I A	6
F I F L R I N E H E T T	4

	Vowels
H I I G F T N G H	2
I N T C V N I E I	4
O T C Y I F Y L H	2
A E A E S N B A E	6
E E E N R W G B N	3
Y D E L R O A E S	4
G R N E B O V N L	2
D A I C A O A L C	5
N D T I R G V A C	2
D O I E S E R E C	5
D V P E I A F I F	4
L R I N E H E T T	3

The vowel count of the lines shows the first arrangement to be the more likely. We will now number the columns and try pairing off certain ones which in no line would give impossible combinations of letters.

The vowel count of the lines indicates that the first arrangement is more likely. We will now number the columns and attempt to pair off certain ones that wouldn’t create impossible letter combinations in any line.

1	2	3	4	5	6	7	8	9	10	11	12
H	I	I	G	F	T	N	G	H	I	N	T
C	V	N	I	E	I	O	T	C	Y	I	F
Y	L	H	A	E	A	E	S	N	B	A	E
E	E	E	N	R	W	G	B	N	Y	D	E
L	R	O	A	E	S	G	R	N	E	B	O
V	N	L	D	A	I	C	A	O	A	L	C
N	D	T	I	R	G	V	A	C	D	O	I
E	S	E	R	E	C	D	V	P	E	I	A
F	I	F	L	R	I	N	E	H	E	T	T

[32]

[__A_TAG_PLACEHOLDER_0__]

These combinations appear among others:

These combinations appear, among others:

1	6	2	4	5	2
H	T	I	G	F	I
C	I	V	I	E	V
Y	A	L	A	E	L
E	W	E	N	R	E
L	S	R	A	E	R
V	I	N	D	A	N
N	G	D	I	R	D
E	C	S	R	E	S
F	I	I	L	R	I

The word FIGHT stares at us from the first line; let us arrange the columns thus:

The word Fight looks at us from the first line; let’s set up the columns like this:

5	2	4	1	6	3
F	I	G	H	T	I
E	V	I	C	I	N
E	L	A	Y	A	H
R	E	N	E	W	E
E	R	A	L	S	O
A	N	D	V	I	L
R	D	I	N	G	T
E	S	R	E	C	E
R	I	L	F	I	F

We have the words FIGHTI(NG), VICIN(ITY), RENEWE(D), ANDVIL(LA), RDINGT(O), RECE(IVED). With this to go on, we must choose column 11 as the next one and then in order, columns 8, 10, 7, 12, 9. But note that the order 11, 8, 10, 7, 12, 9, is the same as the order 5, 2, 4, 1, 6, 3. The message was written in twelve columns and the columns have been transposed in that order. We may, although it is entirely unnecessary, speculate on the key word used. It was probably

We have the words Fighting, Nearby, RENEWED, ANDVIL(LA), RDINGT(O), RECEIVED. With this information, we need to select column 11 as the next one, followed in order by columns 8, 10, 7, 12, and 9. But keep in mind that the order 11, 8, 10, 7, 12, 9, matches the order 5, 2, 4, 1, 6, 3. The message was written in twelve columns and the columns have been rearranged in that sequence. We might, although it’s not necessary, guess the key word used. It was probably

M E X I C O

4 2 6 3 1 5

meaning that the 4th column of the plain text was transferred in enciphering so it became our 1st, the 2d column remained the 2d; the 6th column became our 3d, etc.

meaning that the 4th column of the plain text was transferred in enciphering so it became our 1st, the 2nd column remained the 2nd; the 6th column became our 3rd, etc.

Actually, this cipher was solved because the word VILLA was suspected and all the necessary letters were found in line six of the arrangement in [33]twelve columns. The order 1, 6, 3, 11, 8 was tried and gave this result.

Actually, this cipher was solved because the word VILLA was suspected, and all the needed letters were found in line six of the arrangement in [__A_TAG_PLACEHOLDER_0__] twelve columns. The order 1, 6, 3, 11, 8 was tried and produced this result.

1	6	3	11	8
H	T	I	N	G
C	I	N	I	T
Y	A	H	A	S
E	W	E	D	B
L	S	O	B	R
V	I	L	L	A
N	G	T	O	A
E	C	E	I	V
F	I	F	T	E

The remainder of the solution followed the lines already laid down and, naturally, offered no difficulties, in view of the large number of connected syllables available.

The rest of the solution followed the guidelines already established and, of course, posed no challenges, given the abundance of connected syllables available.

Case 2-b.

Message

Message

SLCOF	WEETN	EBRDO	ORVYM	FFEDI
NMTEC	ROIAR	PERHO	ESETS	RFBHL
TENAH	OPTAU	SOMTL	RTETT	ASCBH
NIODC	RENEN	AAPRD	LACYE	ECIIE
SGUFN

This is a transposition cipher, English text, and contains 105 letters. The factors of 105 are 5 × 3 × 7 so that we must investigate the following rectangles; 5 × 21, 15 × 7, three of 5 × 7, five of 3 × 7 and seven of 5 × 3.

This is a transposition cipher, English text, and contains 105 letters. The factors of 105 are 5 × 3 × 7, so we need to explore the following rectangles: 5 × 21, 15 × 7, three of 5 × 7, five of 3 × 7, and seven of 5 × 3.

21 × 5

Vowels

The vowel count of the columns of the rectangle 5 × 21 is very satisfactory. Let us consider it as three blocks of 5 × 7 each, since we must do this ultimately, and make a vowel count of columns for these blocks.

	5 × 21					Vowels
	S	L	C	O	F	1
	W	E	E	T	N	2
	E	B	R	D	O	2
	O	R	V	Y	M	1
	F	F	E	D	I	2
	N	M	T	E	C	1
	R	O	I	A	R	3
	P	E	R	H	O	2
	E	S	E	T	S	2
	R	F	B	H	L	0
	T	E	N	A	H	2
	O	P	T	A	U	3
	S	O	M	T	L	1
	R	T	E	T	T	1
	A	S	C	B	H	1
	N	I	O	D	C	2
	R	E	N	E	N	2
	A	A	P	R	D	2
	L	A	C	Y	E	2
	E	C	I	I	E	4
	S	G	U	F	N	1
Vowels	7	9	8	7	6

[34]

[__A_TAG_PLACEHOLDER_0__]

	Column
	1	2	3	4	5
Vowels, 1st block	2	2	3	2	2
Vowels, 2d block	2	3	2	2	2
Vowels, 3d block	3	4	3	2	2

This is also excellent, so we will try three blocks 5 × 7 and see if rearrangement of horizontal lines will give results reading the columns vertically.

This is also great, so we will try three blocks 5 × 7 and see if rearranging the horizontal lines will give us results when reading the columns vertically.

1	S L C O F	P E R H O	A S C B H
2	W E E T N	E S E T S	N I O D C
3	E B R D O	R F B H L	R E N E N
4	O R V Y M	T E N A H	A A P R D
5	F F E D I	O P T A U	L A C Y E
6	N M T E C	S O M T L	E C I I E
7	R O I A R	R T E T T	S G U F N

Among other combinations are:

Other combinations include:

3	E B R D O	R F B H L	R E N E N
2	W E E T N	E S E T S	N I O D C
1	S L C O F	P E R H O	A S C B H

5	F F E D I	O P T A U	L A C Y E
7	R O I A R	R T E T T	S G U F N

The addition of line 6 above line 3 and line 4 below line 7 will complete this cipher. The successive columns should be read downward.

The addition of line 6 above line 3 and line 4 below line 7 will complete this cipher. The columns should be read downward in order.

Case 2-c. In this case, both lines and columns are rearranged by means of a key word or key words. The method of solution is the same as Case 2-a and 2-b except that the lines must be rearranged after the columns have been correctly arranged, or in some cases, vice versa. This cipher is not infrequently met with because it seems to offer safety by use of two key words and by the great but only apparent complexity of the method.

Case 2-c. In this case, both rows and columns are rearranged using one or more key words. The method for solving it is the same as in Case 2-a and 2-b, except that the rows need to be rearranged after the columns have been correctly arranged, or in some instances, the other way around. This cipher is often encountered because it seems to provide security through the use of two key words and the significant but only superficial complexity of the method.

Message

Message

WVGAE	EGENL	TFTOH	TEIEF	RBTSE
INENG	ONWRM	GXIXN	GOITN	ROMRO
ESPAL	HNEAC	UDNNH	DERME

This is a transposition cipher, English text and [35]the number of letters, 70, leads us to try rectangles of 10 × 7 and 7 × 10.

This is a transposition cipher, English text and [__A_TAG_PLACEHOLDER_0__]the number of letters, 70, makes us consider rectangles of 10 × 7 and 7 × 10.

	Vowels		Vowels
W V G A E E G E N L	4	W V G A E E G	3
T F T O H T E I E F	3	E N L T F T O	2
R B T S E I N E N G	3	H T E I E F R	3
O N W R M G X I X N	2	B T S E I N E	3
G O I T N R O M R O	4	N G O N W R M	1
E S P A L H N E A C	4	G X I X N G O	2
U D N N H D E R M E	3	I T N R O M R	2
		O E S P A L H	3
		N E A C U D N	3
		N H D E R M E	2

The first form looks the more likely from the vowel count. We proceed to number the columns and lines and try rearrangement of columns so as to obtain possible letter combinations from every line.

The first form seems more probable based on the vowel count. We go ahead and number the columns and rows and attempt to rearrange the columns to generate possible letter combinations from each row.

	1	2	3	4	5	6	7	8	9	10
1	W	V	G	A	E	E	G	E	N	L
2	T	F	T	O	H	T	E	I	E	F
3	R	B	T	S	E	I	N	E	N	G
4	O	N	W	R	M	G	X	I	X	N
5	G	O	I	T	N	R	O	M	R	O
6	E	S	P	A	L	H	N	E	A	C
7	U	D	N	N	H	D	E	R	M	E

Among other combinations we have these:

Among other combinations, we have these:

	3	5	1	4	2	8	10	6	9	7
1	G	E	W	A	V	E	L	E	N	G
2	T	H	T	O	F	I	F	T	E	E
3	T	E	R	S	B	E	G	I	N	N
4	W	M	O	R	N	I	N	G	X	X
5	I	N	G	T	O	M	O	R	R	O
6	P	L	E	A	S	E	C	H	A	N
7	N	H	U	N	D	R	E	D	M	E

A very casual inspection of the lines shows that they should be rearranged in order 6, 1, 2, 7, 3, 5, 4, as follows:

A quick look at the lines suggests that they should be rearranged in this order: 6, 1, 2, 7, 3, 5, 4, as follows:

	3	5	1	4	2	8	10	6	9	7
6	P	L	E	A	S	E	C	H	A	N
1	G	E	W	A	V	E	L	E	N	G
2	T	H	T	O	F	I	F	T	E	E
7	N	H	U	N	D	R	E	D	M	E
3	T	E	R	S	B	E	G	I	N	N
5	I	N	G	T	O	M	O	R	R	O
4	W	M	O	R	N	I	N	G	X	X

Although of no particular importance, it may be stated that the column key in this case was GRAND [36]and the line key was CENTRAL, both used as in enciphering Case 2-a.

Although not particularly significant, it's worth noting that the column key in this case was GREAT [__A_TAG_PLACEHOLDER_0__] and the line key was CENTER, both used for enciphering Case 2-a.

Case 3. Route ciphers. In this case, whole words of the message are transposed according to some of the methods of Case 1 or 2 or their equivalents. The route cipher is little used at present. Its development and use during the Civil War was caused by the inability of the telegraphers of that day to handle regular cipher matter correctly and rapidly. It was, even in those days, frankly only a delaying cipher and, to be of any value, had to be filled with meaningless words to conceal the message proper. An example from the Signal Book will suffice to show the general character of route ciphers. To one familiar with monoliteral transposition ciphers, even the best of route ciphers offers but little difficulty.

Case 3. Route ciphers. In this case, entire words from the message are rearranged using some of the techniques from Case 1 or 2, or their equivalents. Route ciphers are not widely used anymore. Their development and application during the Civil War arose from the difficulties that telegraph operators of that time faced in handling standard cipher text accurately and quickly. Even back then, it was basically just a delaying cipher and needed to be filled with nonsense words to hide the actual message. An example from the Signal Book will demonstrate the general nature of route ciphers. For someone familiar with single-letter transposition ciphers, even the best route ciphers don’t present much of a challenge.

“To encipher the message ‘MOVE DAYLIGHT. ENEMY APPROACHING FROM NORTH. PRISONERS SAY STRENGTH ONE HUNDRED THOUSAND. MEET HIM AS PLANNED.’ arrange as follows:

“To encode the message ‘MOVE DAYLIGHT. ENEMY COMING FROM THE NORTH. PRISONERS REPORT STRENGTH OF ONE HUNDRED THOUSAND. ENGAGE HIM AS PLANNED.’ organize it like this:

MOVE	STRENGTH	PLANNED	SAY
DAYLIGHT	ONE	AS	PRISONERS
ENEMY	HUNDRED	HIM	NORTH
APPROACHING	THOUSAND	MEET	FROM

Here the route is down the first column, up the fourth, down the second and up the third.”

Here, the path is down the first column, up the fourth, down the second, and up the third.”

This cipher was often complicated by the introduction of nulls for every fifth word. Thus the above message might be sent:

This code was often made more complex by adding nulls for every fifth word. So the message above could be sent like this:

MOVE STRENGTH PLANNED SAY NEVER DAYLIGHT ONE AS PRISONERS LEAVING ENEMY HUNDRED HIM NORTH UNCHANGED APPROACHING THOUSAND MEET FROM COME.

The words in italics are nulls and not a part of [37]the message and the receiver eliminates them before arranging his message in columns to get the sense of it.

The words in italics are placeholders and not part of [__A_TAG_PLACEHOLDER_0__]the message, and the receiver removes them before organizing his message in columns to understand it.

As an additional complication, it was customary for each correspondent to have a dictionary or code in which the names of all prominent generals and places and many of the prominent verbs,—as to march, to sail, to encamp, to attack, to retreat,—were represented by other words.

As an added challenge, it was standard for each correspondent to have a dictionary or code that replaced the names of all key generals and locations, as well as many important verbs—like to march, to sail, to camp, to attack, to retreat— with other words.

A route cipher using the code words of the War Department code might have some advantages over the method of enciphering code messages as prescribed in that Code.

A route cipher that uses the code words from the War Department code might have some benefits compared to the method of encoding coded messages as outlined in that Code.

General Remarks on Transposition Ciphers

It is the consensus of opinion of experts that the transposition cipher is not the best one for military purposes. It does not fulfill the first, second, and third of Kerckhoffs’ requirements as to indecipherability, safety when apparatus and method fall into the hands of the enemy, and dependability on a readily changeable key word.

Experts generally agree that the transposition cipher isn't the best choice for military use. It doesn't meet the first, second, and third of Kerckhoffs' requirements for being indecipherable, remaining safe if the equipment and method are captured by the enemy, and relying on an easily changeable keyword.

However, transposition ciphers are often encountered. They are favorites with those who find the substitution ciphers too difficult and too tedious to handle and who believe that their transposition methods are either absolutely indecipherable or sufficiently so for the purpose of concealing the text of a message for the time being. They seem to be particularly popular with secret agents and spies, presumably because special apparatus is rarely necessary in enciphering and deciphering.

However, transposition ciphers are frequently used. They are popular among those who think substitution ciphers are too hard and too tedious to work with and who feel their transposition techniques are either completely unreadable or at least good enough to hide the content of a message for the time being. They seem to be especially favored by secret agents and spies, likely because special equipment is hardly ever needed to encode and decode messages.

Although the number of transposition methods is legion, they can practically all be considered under one of the three cases already discussed. It is surprising how often transposition ciphers prepared [38]by complicated rules, will, on analysis, be seen to be very simple.

Although there are countless transposition methods, almost all of them can be categorized into one of the three cases mentioned earlier. It's surprising how frequently transposition ciphers created [__A_TAG_PLACEHOLDER_0__] using complex rules turn out to be quite simple upon closer examination.

To be successful in solving transposition ciphers, one should constantly practice reading backward and up and down columns, so that the common combinations of letters are as quickly identified when seen thus as when encountered in straight text. Combinations like EHT, LLIW, ROF, DNA, etc., should be appreciated immediately as common words written backward.

To effectively solve transposition ciphers, you should regularly practice reading backwards and scanning up and down columns, so you can quickly recognize common letter combinations just as easily as you would in regular text. Combinations like EHT, LLIW, ROFL, DNA, etc., should be instantly recognized as familiar words written backwards.

A study of the table of frequency of digraphs or pairs is also excellent practice and such a table should be at hand when a transposition cipher is under consideration. It assists greatly if Case 2 be encountered and is of considerable use in solving Case 1.

A study of the frequency table of digraphs or pairs is also great practice, and having such a table available is helpful when looking at a transposition cipher. It is very useful if Case 2 comes up and greatly assists in solving Case 1.

The solution of route ciphers is necessarily one of try and fit, with the knowledge that such ciphers usually are read up and down columns. It is not believed that route ciphers will often be met with at the present day. [39]

The solution to route ciphers primarily involves trial and error, keeping in mind that these ciphers are typically read vertically in columns. It's not thought that route ciphers are commonly encountered nowadays. [__A_TAG_PLACEHOLDER_0__]

Chapter VI

Examination of Substitution Ciphers

When an unknown cipher has been put into the substitution class by the methods already described we may proceed to decide on the variety of substitution cipher which has been used.

When an unknown cipher has been placed into the substitution category using the methods mentioned earlier, we can move forward to determine what type of substitution cipher has been used.

There are a few purely mechanical ways of solving some of the simple cases of substitution ciphers but as a general rule some or all of the following determinations must be made:

There are a few purely mechanical methods for solving some simple cases of substitution ciphers, but generally, some or all of the following determinations need to be made:

1. By preparation of a frequency table for the message we determine whether one or more substitution alphabets have been used and, if one only has been used, this table leads to the solution.

1. By creating a frequency table for the message, we can figure out if one or more substitution alphabets were used, and if only one was used, this table will help us find the solution.

2. By certain rules we determine how many alphabets have been used, if there are more than one, and then isolate and analyze each alphabet by means of a frequency table.

2. Using specific rules, we figure out how many alphabets have been used, especially if there’s more than one, and then we isolate and analyze each alphabet using a frequency table.

3. If the two preceding steps give no results we have to deal with a cipher with a running key, a cipher of the Playfair type, or a cipher where two or more characters are substituted for each letter of the text. Some special cases under this third head will be given but, in general, military ciphers of the substitution class will usually be found to come under the first two heads, on account of the time and care required in the preparation and deciphering of messages by the last named methods and the necessity, in many cases, of using complicated machines for these processes. [40]

3. If the previous two steps don't yield results, we need to deal with a cipher that uses a running key, a Playfair-style cipher, or a cipher where two or more characters are replaced for each letter in the text. Some specific examples under this category will be provided, but generally, military ciphers of the substitution type are typically classified under the first two categories, due to the time and effort needed to prepare and decode messages using the methods mentioned last, as well as the necessity in many instances of employing complex machines for these processes. [__A_TAG_PLACEHOLDER_0__]

Case 4-a.

Message

Message

OBQFO BPBRP QBAML OBHIF PILFQ FJBOX OFLNR BIXOZ EL

From the recurrence of B, F and O, we may conclude that a single substitution alphabet was used for this message. If so and if the alphabet runs in the same order and direction as the regular alphabet, the simplest way to discover the meaning of the message is to take the first two words and write alphabets under each letter as follows, until some line makes sense:

From the repeated appearance of B, F, and O, we can conclude that a single substitution alphabet was used for this message. If that's the case, and if the alphabet follows the same order and direction as the regular alphabet, the easiest way to figure out the meaning of the message is to take the first two words and write alphabets underneath each letter like this, until a line makes sense:

O B Q F O B P B R P

P C R G P C Q C S Q

Q D S H Q D R D T R

R E T I R E S E U S

The word RETIRESE occurs in the fourth line, and, if the whole message be handled in this way we find the rest of the fourth line to read USTED POR EL MISMO ITINERARIO QUE MARCHO. The message was enciphered using an alphabet where A = X, B = Y, C = Z, D = A, etc. noting that as this message is in Spanish the letters K and W do not appear in the alphabet. [41]

The word RETIREMENT appears in the fourth line, and if we decode the entire message this way, the rest of the fourth line reads YOU BY THE SAME ITINERARY AS I MARCHED. The message was encoded using an alphabet where A = X, B = Y, C = Z, D = A, etc., noting that since this message is in Spanish, the letters K and W do not appear in the alphabet. [__A_TAG_PLACEHOLDER_0__]

Case 4-b.

Message

HUJZH UIUPN OZYTS VQXMI SMOMX MQHUD UMREI SESJU AG

This is a message in Spanish. We will handle it as in case 4-a, setting down the whole message.

This is a message in Spanish. We will handle it as in case 4-a, laying out the entire message.

HUJZHUIU	PNOZY	TSV	QX	MISMO	MXMQHUDUMR	EIS	ESJUAG
IVLAIVJV	QOPAZ	UTX	RY	A=A	NYNRIVEVNS	FJT	FTLVBH
JXMBJXLX	RPQBA	VUY	SZ		OZOSJXFXOT	GLU	GUMXCI
LYNCLYMY	SQRCB	XVZ	TA		PAPTLYGYPU	HMV	HVNYDJ
MZODMZNZ	TRSDC	YXA	UB		QBQUMZHZQV	INX	IXOZEL
NAPENAOA	YOU	ZYB	VC		RCRVNAIARX	JOY	JYPAFM
OBQFOBPB	A=U	AZC	XD		SDSXOBJBSY	LPZ	LZQBGN
PCRGPCQC		BAD	YE		TETYPCLCTZ	MQA	MARCHO
QDSHQDRD		CBE	ZF		UFUZQDMDUA	NRB	A=S
RETIRE		DCF	AG		VGVARENEVB	OSC
A=Q		EDG	BH		XHXBSFOFXC	PTD
		FEH	CI		YIYCTGPGYD	QUE
		GFI	DJ		ZJZDUHQHZE	A=O
		HGJ	EL		ALAEVIRIAF
		IHL	A=M		BMBFXJSJBG
		JIM			CNCGYLTLCH
		LJN			DODHZMUMDI
		MLO			EPEIANVNEJ
		NMP			FQFJBOXOFL
		ONQ			GRGLCPYPGM
		POR			HSHMDQZQHN
		A=E			ITINERARY
					A=D

Here each word of the message comes out on a different line, and noting in each case the letter corresponding to A, we have the word QUEMADOS which is the key. The cipher alphabet changed with each word of the message.

Here, each word of the message appears on a separate line, and by noting the letter that corresponds to A in each case, we get the word Burnt, which is the key. The cipher alphabet changes with each word of the message.

A variation of this case is where the cipher alphabet changes according to a key word but the change comes every five letters or every ten letters of the message instead of every word. The text of the message can be picked up in this case with a little study.

A variation of this case is where the cipher alphabet changes based on a keyword, but the change happens every five letters or every ten letters of the message instead of every word. In this case, the text of the message can be deciphered with a bit of study.

Note in using case 4 that if we are deciphering a Spanish message we use the alphabet without K or W as a rule, altho if the letters K or W appear in [42]the cipher it is evidence that the regular English alphabet is used.

Note in using case 4 that if we are decoding a Spanish message, we generally use the alphabet without K or W. However, if the letters K or W appear in [__A_TAG_PLACEHOLDER_0__] the cipher, it indicates that the regular English alphabet is being used.

Case 5-a.

Message

Message

DNWLW MXYQJ ANRSA RLPTE CABCQ RLNEC LMIWL XZQTT QIWRY ZWNSM BKNWR YMAPL ASDAN

This message contains K and W and therefore we expect the English alphabet to be used. The frequency of occurrence of A, L, N, R and W has lead us to examine it under case 4 but without result. Let us set down the first two words and decipher them with a cipher disk set A to A and then proceed as in case 4.

This message includes K and W, so we expect the English alphabet to be used. The frequency of A, L, N, R, and W has led us to look at it in case 4 but with no results. Let's write down the first two words and decode them using a cipher disk set from A to A, then proceed as in case 4.

Cipher message		DNWLWMXYQJ
Deciphered A to	A	XNEPEODCKR
	B	YOFQFPEDLS
	C	ZPGRGQFEMT
	D	AQHSHRGFNU
	E	BRITISHGOV

The message is thus found to be enciphered with a cipher disk set A to E and the text is: BRITISH GOVERNMENT PLACED CONTRACTS WITH FOLLOWING FIRMS DURING SEPTEMBER.

The message is found to be encoded with a cipher disk set A to E, and the text is: THE BRITISH GOVERNMENT AWARDED CONTRACTS TO THE FOLLOWING COMPANIES IN SEPTEMBER..

Case 5-b.

Same as case 4-b except that the cipher message must be deciphered by means of a cipher disk set A to A before proceeding to make up the columns of alphabets. The words of the deciphered message will be found on separate lines, the lines being indicated as a rule by a key word which can be determined as in case 4-b.

Same as case 4-b except that the cipher message has to be decoded using a cipher disk set to A before moving on to create the columns of alphabets. The words from the decoded message will appear on separate lines, typically indicated by a keyword that can be figured out as in case 4-b.

The question of alphabetic frequency has already been discussed in considering the mechanism of language. It is a convenient thing to put the frequency tables in a graphic form and to use a similar graphic form in comparing unknown alphabets with the standard frequency tables. For instance the standard Spanish frequency table put in graphic [43]form is here presented in order to compare with it the frequency table for the message discussed in case 4-a.

The question of letter frequency has already been talked about when looking at how language works. It’s useful to display the frequency tables visually and to use a similar visual format to compare unknown alphabets with the standard frequency tables. For example, the standard frequency table for Spanish is presented in a graphic [__A_TAG_PLACEHOLDER_0__]form here to compare it with the frequency table for the message discussed in case 4-a.

Standard Spanish frequency table			Table for Message Case 4-a
A	111111111111111111111111111	27	A	1	1
B	11	2	B	1111111	7
C	111111111	9	C
D	1111111111	10	D
E	1111111111111111111111111111	28	E	1	1
F	11	2	F	11111	5
G	111	3	G
H	11	2	H	1	1
I	111111111111	12	I	111	3
J	1	1	J	1	1
L	1111111111	10	L	111	3
M	111111	6	M	1	1
N	111111111111	12	N	1	1
O	1111111111111111	16	O	111111	6
P	11111	5	P	111	3
Q	11	2	Q	111	3
R	111111111111111	15	R	11	2
S	11111111111111	14	S
T	11111111	8	T
U	1111111	7	U
V	11	2	V
X			X	11	2
Y	11	2	Y
Z	1	1	Z	1	1

Our first assumption might be that B = A and F = E but it is evident at once that in that case, S, T, U and V (equal to R, S, T and U) do not occur and a message even this short without R, S, T or U is practically impossible. By trying B = E we find that the two tables agree in a general way very well and this is all that can be expected with such a short message. The longer the message the nearer would its frequency table agree with the standard table. Note that if a cipher disk has been used, the alphabet runs the other way and we must count upward in working with a graphic table. Note also that if, in a fairly long message, it is impossible to coördinate the graphic table, reading either up or down, with the standard table and yet some letters occur much more frequently than others and some do not occur at all, we have a mixed alphabet to deal with. The example chosen for case 6-a is of this character. An examination of the frequency table given under that case shows that it bears no graphic resemblance to [44]the standard table. However, as will be seen in case 7-b, the preparation of graphic tables enables us to state definitely that the same order of letters is followed in each of a number of mixed alphabets.

Our first assumption might be that B = A and F = E, but it’s clear right away that in that case, S, T, U, and V (which are equal to R, S, T, and U) do not appear, and having a message this short without R, S, T, or U is practically impossible. By trying B = E, we find that the two tables generally match up quite well, which is all we can expect with such a short message. The longer the message, the closer its frequency table would align with the standard table. Keep in mind that if a cipher disk is used, the alphabet runs backward, and we have to count upward when working with a graphic table. Also, if in a reasonably long message, it’s impossible to coordinate the graphic table, whether reading up or down, with the standard table, and yet some letters appear much more frequently than others while some don’t appear at all, we’re dealing with a mixed alphabet. The example chosen for case 6-a fits this description. An examination of the frequency table shown in that case indicates that it does not visually resemble [__A_TAG_PLACEHOLDER_0__] the standard table. However, as will be shown in case 7-b, preparing graphic tables allows us to clearly state that the same order of letters is followed in each of several mixed alphabets.

General Remarks

Any substitution cipher, enciphered by a single alphabet composed of letters, figures or conventional signs, can be handled by the methods of case 6. For example, the messages under case 4-a and 5-a are easily solved by these methods. But note that the messages under case 4-b and 5-b cannot so be solved because several alphabets are used. We will see later that there are methods of segregating the different alphabets in some cases where several are used and then each of the alphabets is to be handled as below.

Any substitution cipher, encoded with a single alphabet made up of letters, numbers, or standard symbols, can be managed using the techniques in case 6. For instance, the messages in case 4-a and 5-a can be easily solved with these methods. However, keep in mind that the messages in case 4-b and 5-b cannot be solved this way because they use multiple alphabets. We will later explore methods to separate the different alphabets in instances where multiple ones are used, allowing each alphabet to be addressed as described below.

Case 6-a.

Message

Message

QDBYP BXHYS OXPCP YSHCS EDRBS ZPTPB BSCSB PSHSZ AJHCD OSEXV HPODA PBPSZ BSVXY XSHCD

This message was received from a source which makes us sure it is in Spanish. The occurrence of B, H, P and S has tempted us to try the first two words as in case 4 and 5 but without result. We now prepare a frequency table, noting at the same time the preceding and following letter. This latter proceeding takes little longer than the preparation of an ordinary frequency table and gives most valuable information. [45]

This message came from a source that confirms it's in Spanish. The appearance of B, H, P, and S encouraged us to attempt the first two words as in cases 4 and 5, but we had no luck. We're now creating a frequency table, while also noting the before and following letters. This process takes a bit longer than making a standard frequency table, but it provides very valuable information. [__A_TAG_PLACEHOLDER_0__]

Frequency Table

Frequency Chart

		Prefix		Suffix
A	11	2	ZD	JP
B	11111111	8	DPRPBSPZ	YXSBSPPS
C	11111	5	PHSHH	PSSDD
D	11111	5	QECOC	BROA
E	11	2	SS	DX
F
G
H	111111	6	XSSJVS	YCSCPC
I
J	1	1	A	H
L
M
N
O	111	3	SDP	XSD
P	111111111	9	YXCZTBHAB	BCYTBSOBS
Q	1	1		D
R	1	1	D	B
S	111111111111	12	YYCBBCPHOPBX	OHEZCBHZEZVH
T	1	1	P	P
U
V	11	2	XS	HX
X	11111	5	BOEVY	HPVYS
Y	1111	4	BHPX	PSSX
Z	111	3	SSS	PAB

It is clear from an examination of this table that we have to deal with a single alphabet but one in which the letters do not occur in their regular order.

It’s evident from looking at this table that we are dealing with a single alphabet, but the letters aren’t arranged in their usual order.

We may assume that P and S are probably A and E, both on account of the frequency with which they occur and the variety of their prefixes and suffixes. If this is so, then B and H, are probably consonants and may represent R and N respectively. D and X are then vowels by the same method of analysis. Noting that HC occurs three times and taking H as N we conclude that C is probably T. Substitute these values in the last three words of [46]the message because the letters assumed occur rather frequently there.

We can assume that P and S are likely A and E, based on how often they appear and the range of their prefixes and suffixes. If that’s the case, then B and H are probably consonants and might stand for R and N respectively. D and X are then vowels using the same method of analysis. Noticing that HC appears three times and assuming H is N, we conclude that C is likely T. Use these values in the last three words of [__A_TAG_PLACEHOLDER_0__]the message since the letters we're assuming show up quite often there.

PBPSZBSV	X	Y	X	SHC	D
	I		I		I
ARAE_RE_		_		ENT
	O		O		O

Now Z is always prefixed by S and may be L. Taking X=I and D=O, (they are certainly vowels), V=G and Y=M, we have

Now Z is always preceded by S and can be L. By using X=I and D=O, (which are definitely vowels), V=G and Y=M, we have

ARA EL REGIMIENTO

Substituting these values in the rest of the message we have

Substituting these values in the rest of the message, we have

Q	DBYPBXH	YSOXPCP	YSHCSED	RBSZPTPB
_	ORMARIN	ME_IATA	MENTE_O	_RELA_AR

	BSCSB	PSHSZ	AJHCD	OSEXVHPODA
	RETER	AENEL	__NTO	_E_IGNA_O_

We may now take Q=F, O=D, E=S, R=B, T=C, A=P and J=U and the message is complete. We are assisted in our last assumption by noting that S=E and E=S, etc., and we may on that basis reconstruct the entire alphabet. The letters in parenthesis do not occur in the message but may be safely assumed to be correct.

We can now take Q=F, O=D, E=S, R=B, T=C, A=P, and J=U, and the message is complete. Our final assumption is supported by noticing that S=E and E=S, and based on that, we can reconstruct the entire alphabet. The letters in parentheses do not appear in the message but can be assumed to be correct.

Ordinary

Cipher

(Q)

(V)

(X)

(U)

(Z)

(Y)

(H)

It is always well to attempt the reconstruction of the entire alphabet for use in case any more cipher messages written in it are received.—— [47]

It’s always a good idea to try to reconstruct the entire alphabet for use in case any more coded messages written in it come in.—— [__A_TAG_PLACEHOLDER_0__]

Case 6-b.

Message

Lt. J. B. Smith, Royal Flying Corps, Calais, France.

DACFT	RRBHA	MOOUE	AENOI	ZTIET
ASMOS	EOHIE	YOCKF	NOHOE	NOUTH
OMEAH	NILGO	OSAHU	OHOUE	APCHS
TLNDA	CFTEN	INTWN	BAFOH	GROHT
AEIOH	ABRIS	ODACF	TRREN	OSTSM
AYBIS	DFTEN	EFAPH	OSMNI	ZTIEA
HLILL	TWSOU	GDENO	UTHOM	EAHBH
AMOOU	EAYOE	QISUU	OLEHA	DENOE
NHOOQ	OBBOR	TSLHO	BAHEO	UBHOB
IHTSW	ENOHO	PAHIH	ITUAS	BIHTL

Graham-White.

The address and signature indicate that this message is in English.

The address and signature show that this message is in English.

There are 250 letters in the cipher; the vowels AEIOU occur 109 times or 43.6%, the letters LNRST occur 62 times or 24.8%, and the letters KQVXZ occur 5 times or 2%. The proportion in the case of the vowels is somewhat too large and, in the case of the letters LRNST, it is too small. It is then questionable whether this is a transposition cipher altho, at first glance it might appear to be one.

There are 250 letters in the cipher; the vowels AEIOU appear 109 times or 43.6%, the letters LNRST appear 62 times or 24.8%, and the letters KQVXZ appear 5 times or 2%. The proportion of the vowels is a bit too high, while the frequency of the letters LRNST is too low. This raises doubts about whether this is a transposition cipher, although it might seem like one at first glance.

On examination for parts of possible words we are at once struck by the occurrence at irregular intervals of recurring groups, viz:

On examining parts of possible words, we're immediately struck by the occasional appearance of recurring groups, namely:

DACFTRR	ENO	BHAMOOUEA
DACFTEN	ENOUTHOMEAH	BHAMOOUEA
	ENO
DACFTRR	DENOUTHOMEAH	IZTIE
FTEN	DENO	IZTIE
	ENO

This is a strong indication that the cipher is a substitution cipher, so, to make an examination a frequency table will be constructed.

This strongly suggests that the cipher is a substitution cipher, so to analyze it, a frequency table will be created.

Frequency Table

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
23	11	7	6	24	7	3	26	16	0	1	8	8	15	36	3	2	8	14	17	11	1	3	0	3	2

[48]

[__A_TAG_PLACEHOLDER_0__]

Superficially, this looks like a normal frequency table, but O is the dominant letter, followed by H, E, A, T, I, N, S, in the order named. It is certainly Case 6 if it is a substitution cipher at all.

Superficially, this looks like a regular frequency table, but O is the most common letter, followed by H, E, A, T, I, N, S, in that order. It definitely counts as Case 6 if it is a substitution cipher at all.

Let us see what can be done by assuming O=E; the triplet ENO, occurring six times might well be THE and E=T and N=H. A glance at the frequency table shows this to be reasonable. Now substitute these letters in some likely groups. FNOHOENO becomes _HE_ETHE; FTEN becomes _TH; ENOENHO becomes THETH_E; ENOHO becomes THE_E. A bit of study will show that F=W, T=I and H=R and the frequency table bears this out except that H(=R) seems to occur too frequently. The recurring groups containing DAC (see above) occur in such a way that we may be sure DAC is one word, FTRR is another and FTEN(=WITH) is a third. Now FTRR becomes WI__, which can only be completed by a double letter. LL fills the bill and we may say R=L. As DAC starts the message and is followed by FTRR (=WILL) it is reasonable to try DAC=YOU. Looking up DAC in the frequency table it is evident that we strain nothing by this assumption. We now have:

Let’s see what we can find by assuming O=E; the triplet ENO, which appears six times, could very well be THE and E=T and N=H. A look at the frequency table suggests this makes sense. Now, let’s replace these letters in some likely combinations. FNOHOENO becomes _HE_ETHE; FTEN becomes _TH; ENOENHO becomes THETH_E; ENOHO becomes THE_E. With some analysis, we’ll see that F=W, T=I, and H=R, and the frequency table supports this, except that H(R) seems to occur a bit too often. The repeating groups with Digital-to-Analog Converter (see above) occur in such a way that we can be sure DAC is one word, FTRR is another, and FTEN(=WITH) is a third. Now, FTRR becomes WI__, which can only be completed by a double letter. LL fits this, so we can say R=L. Since DAC starts the message and is followed by FTRR (WILL), it makes sense to try DAC=YOU. Looking up DAC in the frequency table, it’s clear that this assumption isn’t a stretch. We now have:

Letters of cipher	ONTAHECFD
Letters of message	EHIORTUWY

Now take the group ENOUTHOMEAH which occurs twice. This becomes THE_IRE_TOR and if we substitute U=D and M=C we have THE DIRECTOR. Next the group (FTRR)BHAMOOUEA becomes (WILL) _ROCEEDTO and the context gives word with missing letter as PROCEED, from which B=P. Next the group (ENO) IZTIETASMOSEOHIEYOCK(FNOHO) becomes (THE)__I_TIO_CE_TER_T_EU_(WHERE) and the group (FTEN)EFAPHOSMNIZTIEAHL becomes (WITH)TWO_RE_CH__I_TOR_. [49]The substitution of A for I, V for Z, N for S and F for P makes the latter group read (WITH TWO FRENCH AVIATORS and the former read (THE)AVIATION CENTER AT _EU_(WHERE).

Now take the group ENOUTHOMEAH which appears twice. This becomes THE_IRE_TOR and if we substitute U=D and M=C, we get THE DIRECTOR. Next, the group (FTRR)BHAMOOUEA becomes (WILL) _PROCEEDTO and the context provides a word with a missing letter as Understood. Please provide the text you'd like me to modernize., from which B=P. Next, the group (ENO) IZTIETASMOSEOHIEYOCK(FNOHO) becomes (THE)__I_TIO_CE_TER_T_EU_(WHERE) and the group (FTEN)EFAPHOSMNIZTIEAHL becomes (WITH)TWO_RE_CH__I_TOR_. [__A_TAG_PLACEHOLDER_0__] The substitution of A for I, V for Z, N for S, and F for P makes the latter group read (WITH TWO FRENCH PILOTS and the former read Aviation Center at _EU_ (Where).

Now the word YOCK = (_EU_) is the name of a place, evidently. We find another group containing Y, viz: ENOSTSMAYBISD which becomes THENINCO_PANY so that evidently we should substitute M for Y. The other occurrence of Y (=M) is in the group EAYOEQISU which becomes TOMET_AND. A reasonable knowledge of geography gives us the words MEUX and METZ so that X should be substituted for K and Z for Q.

Now the word YOCK = (_EU_) is clearly the name of a place. We find another group containing Y, namely: ENOSTSMAYBISD which turns into THENINCO_COMPANY, so it seems we should replace M with Y. The other time Y (=M) appears is in the group EAYOEQISU, which becomes TOMET_AND. A good understanding of geography gives us the words MEUX and METZ, meaning that X should replace K and Z should replace Q.

We now have sufficient letters for a complete deciphering of the message.

We now have enough letters to completely decode the message.

Letters of cipher	ABCDEFGHIKLMNOPQRSTUVWYZ
Letters of message	OPUYTW_RAXSCHEFZLNID__MV

The message deciphers:

The message decodes:

YOU WILL PROCEED TO THE AVIATION CENTER AT MEUX WHERE THE DIRECTOR HAS _EEN ORDERED TO FURNISH YOU WITH A HI_H POWER _LERIOT AEROPLANE. YOU WILL THEN IN COMPANY WITH TWO FRENCH AVIATORS ASSI_NED _Y THE DIRECTOR PROCEED TO METZ AND DESTROY THE THREE ZEPPELINS REPORTED PREPARIN_ THERE FOR A RAID ON PARIS.

You will go to the aviation center at Meux, where the director has been instructed to provide you with a high-power Bleriot airplane. Together with two French pilots assigned by the director, you will then head to Metz to destroy the three Zeppelins that are reportedly getting ready for a raid on Paris.

The substitution of B for G, G for W and K for V completes the cipher. This cipher is difficult only because the cipher alphabet is made up, not haphazard, but scientifically with proper consideration for the natural frequency of occurrence of the letters. In cipher work it is dangerous to neglect proper analysis and jump at conclusions.

The replacement of B with G, G with W, and K with V completes the cipher. This cipher is challenging mainly because the cipher alphabet is created deliberately, not randomly, but thoughtfully based on the natural frequency of how letters appear. In cipher work, it's risky to ignore proper analysis and jump to conclusions.

In the study of Mexican substitution ciphers, several alphabets have been found which are made up in a general way, like the one discussed in this case.

In the study of Mexican substitution ciphers, several alphabets have been discovered that are generally created in a similar way to the one discussed in this case.

[50]

[__A_TAG_PLACEHOLDER_0__]

Case 6-c.—It is a convenience in dealing with ciphers made up of numbers or conventional signs to substitute arbitrary letters for the numbers and signs. Suppose we have the message:

Case 6-c.—It's easier to work with ciphers that consist of numbers or symbols if we replace those numbers and symbols with random letters. Let's say we have the message:

”??2&	45x15	)“8&#	&&1x4	%&4&%
6x?&”	8&*x4	6°*°&	%“4&”

By arbitrary substitution of letters this is made

By randomly replacing letters, this is done.

ABBCD	EFGHF	IJKDL	DDHGE	MDEDM
NGBDA	KDOGE	NPOPD	MAEDA

This message is now in convenient shape to handle as Case 6-a and on solution is found to read:

This message is now easy to manage as Case 6-a, and the solution is found to read:

ALL PERSONS HAVE BEEN ORDERED TO LEAVE FORTIFIED AREA.

Everyone has been instructed to leave the protected area.

In the same way the message

1723	3223	2825	1828	3630	2336	1423	2827	2324	3120	2317	3123
3036	2120	2415	3029	1512	2831	1721	2715	2811	2715	1923	3030
1215	1130	2128	3623

is found to be made up entirely of numbers between 11 and 36 with the numbers 23, 28 and 30 occurring most frequently. This immediately suggests an alphabet made up of the numbers from 11 to 36 inclusive and each cipher group of figures represents two letters. By arbitrary substitution of letters for groups of two numbers we obtain:

is found to consist entirely of numbers between 11 and 36, with the numbers 23, 28, and 30 appearing most often. This clearly indicates an alphabet comprised of the numbers from 11 to 36, and each group of two numbers represents two letters. By randomly substituting letters for groups of two numbers, we get:

AB	CB	DE	FD	GH	BG	IB	DJ	BK	LM	BA	LB
HG	NM	OP	HQ	PR	DL	AN	JP	DS	JP	TB	HH
RP	SH	ND	GB

and this message is also in shape to handle as Case 6-a. It reads, on solution,

and this message is also formatted to handle as Case 6-a. It says, upon resolution,

SEVEN HUNDRED MEN LEFT YESTERDAY FOR POINTS ON LOWER RIO GRANDE.

Seven hundred men left yesterday for locations on the lower Rio Grande.

[51]

[__A_TAG_PLACEHOLDER_0__]

Chapter VII

We will now consider the class of substitution ciphers where a number of alphabets are used, the number and choice of alphabets depending on a key word or equivalent and being used periodically throughout the message.

We will now look at the type of substitution ciphers that use multiple alphabets. The number and selection of these alphabets depend on a keyword or similar, and they are used periodically throughout the message.

In this class belong the methods of Vigenere, Porta, Beaufort, St. Cyr, and many others. These methods date back several hundred years, but variations of them are constantly appearing as new ciphers. The Larrabee cipher, used for communication between government departments, is the Vigenere cipher of the 17th Century. The cipher disk method is practically the Vigenere cipher with reversed alphabets.

In this class are the methods of Vigenere, Porta, Beaufort, St. Cyr, and many others. These methods go back several hundred years, but new variations keep emerging as modern ciphers. The Larrabee cipher, used for communication between government departments, is essentially the Vigenere cipher from the 17th century. The cipher disk method is basically the Vigenere cipher with reversed alphabets.

In using these ciphers, there is provided a number of different cipher alphabets, usually twenty-six, and each cipher alphabet is identified by a different letter or number. A key word or phrase (or key number) is agreed upon by the correspondents. The message to be enciphered is written in lines containing a number of letters which is a multiple of the number of letters of the key. The key is written as the first line. Then each column under a letter of the key is enciphered by the cipher alphabet pertaining to that letter of the key. For example, let us take the message, “All radio messages must hereafter be put in cipher,” with the key Grant, using the Vigenere cipher alphabets given below. Each of these alphabets is identified by the first or left hand letter which represents A of the text. We thus will [52]use in turn the alphabets beginning with G, with R, with A, with N, and with T.

In using these ciphers, there are several different cipher alphabets, usually twenty-six, and each alphabet is labeled by a specific letter or number. A key word or phrase (or key number) is agreed upon by those communicating. The message that needs to be enciphered is written in lines that contain a number of letters that is a multiple of the length of the key. The key is written as the first line. Then, each column below a letter of the key is enciphered using the cipher alphabet corresponding to that letter of the key. For example, let's take the message, “All radio messages must hereafter be put in cipher,” with the key Grant, using the Vigenere cipher alphabets provided below. Each of these alphabets is identified by the first or leftmost letter which represents A of the text. We will [__A_TAG_PLACEHOLDER_0__] use in sequence the alphabets starting with G, then with R, followed by A, then N, and finally T.

G	R	A	N	T	G	R	A	N	T

A	L	L	R	A	D	I	O	M	E
S	S	A	G	E	S	M	U	S	T
H	E	R	E	A	F	T	E	R	B
E	P	U	T	I	N	C	I	P	H
E	R

Using the alphabet indicated by G, we get

G	J
Y	Y
N	L
K	T
K

Continuing for the other alphabets, we get

Continuing with the other letters, we get

G	C	L	E	T	J	Z	O	Z	X
Y	J	A	T	X	Y	D	U	F	M
N	V	R	R	T	L	K	E	E	U
K	G	U	G	B	T	T	I	C	A
K	I

This method of arranging the message into lines and columns and then enciphering whole columns with each cipher alphabet is much shorter than the method of handling each letter of the message separately. The chance of error is also greatly reduced.

This way of organizing the message into lines and columns and then encoding entire columns with different cipher alphabets is much quicker than dealing with each letter of the message one at a time. The likelihood of making mistakes is also significantly lower.

All these cipher methods can be operated by means of squares containing the various alphabets, cipher disks or arrangements of fixed and sliding alphabets. For example, this was the original cipher of Vigenere: [53]

All these cipher methods can be used with squares that have different alphabets, cipher disks, or setups of fixed and movable alphabets. For example, this was the original cipher of Vigenère: [__A_TAG_PLACEHOLDER_0__]

The first horizontal alphabet is the alphabet of the plain text. Each substitution alphabet is designated by the letter at the left of a horizontal line. For example, if the key word is BAD, the second, first and fourth alphabets are used in turn and the word WILL is enciphered XIOM.

The first horizontal alphabet is the plain text alphabet. Each substitution alphabet is indicated by the letter to the left of a horizontal line. For example, if the keyword is AWFUL, the second, first, and fourth alphabets are used in sequence to encipher the word WILL as XIOM.

The Larrabee cipher is merely a slightly different arrangement of the Vigenere cipher and is printed on a card in this form: [54]

The Larrabee cipher is just a slightly different version of the Vigenere cipher and is printed on a card like this: [__A_TAG_PLACEHOLDER_0__]

A	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	abcdefghijklmnopqrstuvwxyz
B	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	bcdefghijklmnopqrstuvwxyza
C	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	cdefghijklmnopqrstuvwxyzab
etc.
Y	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	yzabcdefghijklmnopqrstuvwx
Z	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	zabcdefghijklmnopqrstuvwxy

The large letters at the left are the letters of the key word. It will be noted that these letters correspond to the first letters of the cipher alphabets (in small letters) as in the Vigenere cipher.

The big letters on the left are the letters of the key word. You'll notice that these letters match the first letters of the cipher alphabets (in lowercase) as found in the Vigenere cipher.

A much simpler arrangement of the Vigenere cipher is the use of a fixed and sliding alphabet. Either the fixed or sliding alphabet must be double in order to get coincidence for every letter when A is set to the letter of the key word.

A much simpler version of the Vigenere cipher is to use a fixed and sliding alphabet. Either the fixed or sliding alphabet needs to be doubled to ensure a match for every letter when A is aligned with the letter of the key word.

Fixed Alphabet of Text
ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ
	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	Movable Alphabet of Cipher

As shown here, A of the fixed or text alphabet coincides with T of the movable cipher alphabet. This is the setting where T is the letter of the key word in use. The lower movable alphabet is moved for each letter of the message and the A of the fixed alphabet is made to coincide in turn with each letter of the key before the corresponding letter of the text is enciphered. It is obviously only a step from this arrangement to that of a cipher disk, where the [55]fixed alphabet, (a single one will now serve) is printed in a circle and the movable alphabet, also in a circle, is on a separate rotatable disk. Coincidence of any letter on the disk with A of the fixed alphabet is obtained by rotating the disk.

As shown here, A of the fixed or text alphabet lines up with T of the movable cipher alphabet. This setup means that T is the letter from the keyword that's currently in use. The lower movable alphabet shifts for each letter of the message, and the A from the fixed alphabet is aligned with each letter of the keyword before the corresponding letter of the text is encoded. It's clear that this arrangement is just a step away from using a cipher disk, where the [__A_TAG_PLACEHOLDER_0__]fixed alphabet (a single one is sufficient now) is printed in a circle, and the movable alphabet, also in a circle, is on a separate rotating disk. You achieve the alignment of any letter on the disk with A of the fixed alphabet by rotating the disk.

The well known U. S. Army Cipher Disk has just such an arrangement of the fixed alphabet but the alphabet of the disk is reversed. This has several advantages in simplicity of operation but none in increasing the indecipherability of the cipher prepared with it. The arrangement of fixed and sliding alphabets which is equivalent to the U. S. Army cipher disk is this:

The well-known U.S. Army Cipher Disk has a similar setup with a fixed alphabet, but the alphabet on the disk is flipped. This offers a few benefits for ease of use, but it doesn't do anything to make the resulting cipher harder to crack. The setup of the fixed and sliding alphabets that is equivalent to the U.S. Army cipher disk is this:

Fixed Alphabet
ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ
	ZYXWVUTSRQPONMLKJIHGFEDCBA
	Movable Alphabet

It will be noticed that with this arrangement of running the alphabets in opposite directions, it becomes immaterial which alphabet is used for the text and which for the cipher for if A = G then G = A. This is not true of the Vigenere cipher.

It will be noticed that with this setup of running the alphabets in opposite directions, it doesn't matter which alphabet is used for the text and which for the cipher, because if A = G, then G = A. This is not the case with the Vigenere cipher.

It is perfectly feasible to substitute a card for the U. S. Army cipher disk. It would have this form:

It is completely possible to replace a card with the U.S. Army cipher disk. It would look like this:

	ABCDEFGHIJKLMNOPQRSTUVWXYZ
1	AZYXWVUTSRQPONMLKJIHGFEDCB
2	BAZYXWVUTSRQPONMLKJIHGFEDC
3	CBAZYXWVUTSRQPONMLKJIHGFED
etc.
25	YXWVUTSRQPONMLKJIHGFEDCBAZ
26	ZYXWVUTSRQPONMLKJIHGFEDCBA

The first horizontal line is the alphabet of the text. The other twenty-six lines are the cipher alphabets each corresponding to the letter of the key word which is at the left of the line. [56]

The first horizontal line is the alphabet of the text. The other twenty-six lines are the cipher alphabets, each matching the letter of the keyword on the left side of the line. [__A_TAG_PLACEHOLDER_0__]

One of the ciphers of Porta was prepared with a card of this kind:

One of Porta's ciphers was created using a card like this:

AB	ABCDEFGHIJKLM
	NOPQRSTUVWXYZ
CD	ABCDEFGHIJKLM
	ZNOPQRSTUVWXY
EF	ABCDEFGHIJKLM
	YZABCDEFGHIJK
etc.
WX	ABCDEFGHIJKLM
	PQRSTUVWXYZNO
YZ	ABCDEFGHIJKLM
	OPQRSTUVWXYZN

In this cipher the large letters at the left correspond to the letters of the key and, in each alphabet, the lower letter is substituted for the upper and vice versa. For example, with key BAD to encipher WILL we would get JVXY. Note that with either B or A as the key letter, the first alphabet would be used.

In this cipher, the uppercase letters on the left match the letters of the key, and in each alphabet, the lowercase letter is swapped for the uppercase and vice versa. For instance, using the key NOT GOOD to encode WILL would give us JVXY. Keep in mind that if either B or A is chosen as the key letter, the first alphabet will be used.

A combination of the Vigenere and Porta ciphers is this:

A mix of the Vigenère and Porta ciphers is this:

A	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	ABCDEFGHIJKLMNOPQRSTUVWXYZ
BC	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	BCDEFGHIJKLMNOPQRSTUVWXYZA
DE	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	CDEFGHIJKLMNOPQRSTUVWXYZAB
etc.
VW	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	LMNOPQRSTUVWXYZABCDEFGHIJK
XY	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	MNOPQRSTUVWXYZABCDEFGHIJKL
Z	ABCDEFGHIJKLMNOPQRSTUVWXYZ
	NOPQRSTUVWXYZABCDEFGHIJKLM

[57]

[__A_TAG_PLACEHOLDER_0__]

Here again the large letters at the left correspond to the letters of the key and, in each pair of alphabets, the upper one is that of the plain text and the lower is that of the cipher.

Here again, the large letters on the left match the letters of the key, and in each pair of alphabets, the upper one represents the plain text and the lower one represents the cipher.

This cipher can also be operated by a fixed and sliding alphabet.

This cipher can also be used with a fixed and sliding alphabet.

Fixed Alphabet

ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZ

ABCDEFGHIJKLMNOPQRSTUVWXYZ

Sliding Alphabet of Cipher

\/ Index

	BDFHJLNPRTVX
A		Z	Letters of Key.
	CEGIKMOQSUWY

The other ciphers mentioned are merely variations of these that have been discussed. It is immaterial, in the following analysis, which variety has been used. The analysis is really based on what can be done with a cipher made up with a mixed cipher alphabet which may be moved with reference to the fixed alphabet of the text, (See Case 7-b). Clearly this is a much more difficult proposition than dealing with a cipher in which the cipher alphabets run in their regular sequence, either backward or forward. In fact, in the analysis of Case 7, we may consider any cipher prepared by the method of Vigenere or any of its variations as a special and simple case.

The other ciphers mentioned are just variations of the ones we've talked about. For the following analysis, it doesn't matter which version has been used. The analysis really focuses on what can be done with a cipher that uses a mixed cipher alphabet that can be shifted in relation to the fixed alphabet of the text, (See Case 7-b). Clearly, this is a much more challenging task than working with a cipher where the cipher alphabets follow their usual order, either backward or forward. In fact, in the analysis of Case 7, we can treat any cipher created using the Vigenere method or its variations as a special and straightforward case.

It was long ago discovered that, in any cipher of this class, (1) two like groups of letters in the cipher are most probably the result of two like groups of letters of the text enciphered by the same alphabets and (2) the number of letters in one group plus the number of letters to the beginning of the second group is a multiple of the number of alphabets used. It is evident, of course, that we may have similar groups in the cipher which are not the result of enciphering [58]similar groups of the text by the same alphabets but if we take all recurring groups in a message and investigate the number of intervening letters, we will find that the majority of such cases will conform to these two principles.

It was long ago discovered that, in any cipher of this kind, (1) two identical groups of letters in the cipher are most likely the result of two identical groups of letters from the text encoded with the same alphabets and (2) the number of letters in one group plus the number of letters before the second group is a multiple of the number of alphabets used. It is clear, of course, that we may have similar groups in the cipher that do not stem from encoding [__A_TAG_PLACEHOLDER_0__] similar groups of the text with the same alphabets, but if we look at all recurring groups in a message and examine the number of letters in between, we will find that most of these cases will follow these two principles.

Changing the key word and message to illustrate more clearly the above points, the following is quoted from the Signal Book, 1914, with reference to the use of the cipher disk in preparing a message with a key word.1

Changing the key word and message to better illustrate the points above, the following is quoted from the Signal Book, 1914, regarding the use of the cipher disk in creating a message with a key word.1

“—This simple disk can be used with a cipher word or, preferably, cipher words, known only to the correspondents.... Using the key word ‘disk’ to encipher the message ‘Artillery commander will order all guns withdrawn,’ we will proceed as follows: Write out the message to be enciphered and above it write the key word ... letter over letter, thus:


DISK	DISK	DISK	DISK	DISK	DISK	DISK	DISK	DISK	DISK	DIS
ARTI	LLER	YCOM	MAND	ERWI	LLOR	DERA	LLGU	NSWI	THDR	AWN

DRZC	SXOT	FGEY	RIFH	ZRWC	SXET	AEBK	SXMQ	QQWC	XBPT	DMP

“Now bring the ‘a’ of the upper disk under the first letter of the key word on the lower disk, in this case ‘D’. The first letter of the message to be enciphered is ‘A’: ‘d’ is found to be the letter connected with ‘A’, and it is put down as the first cipher letter. The letter ‘a’ is then brought under ‘I’ which is the second letter of the key word. ‘R’ is to be enciphered and ‘r’ is found to be the second cipher letter.... Proceed in this manner until the last letter of the key word is used and beginning again with the letter ‘D’, so continue until all letters of [59]the message have been enciphered. Divided into groups of five letters, it will be as follows:

“Now bring the ‘a’ of the upper disk under the first letter of the keyword on the lower disk, which is ‘D’ in this case. The first letter of the message to be encoded is ‘A’: ‘d’ is connected with ‘A’, so it becomes the first cipher letter. Next, place the letter ‘a’ under ‘I’, the second letter of the keyword. ‘R’ needs to be encoded, and ‘r’ is identified as the second cipher letter.... Continue this way until you've used the last letter of the keyword, then start over with the letter ‘D’, and keep going until all letters of [__A_TAG_PLACEHOLDER_0__]the message have been encoded. Split into groups of five letters, it will look like this:

“DRZCS XOTFG EYRIF HZRWC SXETA EBKSX MQQQW CKBPT DMF.”

So much for the Signal Book; now let us examine the above message for pairs or similar groups and count the intervening letters to demonstrate principles (1) and (2);

So much for the Signal Book; now let's take a look at the message above for pairs or similar groups and count the letters in between to illustrate principles (1) and (2);

CSX	—	CSX	16	=	4 × 4
SX	—	SX	16	=	4 × 4
SX	—	SX	8	=	2 × 4
WC	—	WC	16	=	4 × 4

The key word might contain 2, 4 or 8 letters from the evidence but we may eliminate 2 as unlikely and preparation of frequency tables of each of the four alphabets would soon show that 4 is the correct number.

The key word might have 2, 4, or 8 letters from the evidence, but we can rule out 2 as unlikely, and creating frequency tables for each of the four alphabets would quickly reveal that 4 is the correct number.

A later and more extensive example (Case 7-a) will show pairs not separated by multiples of the number of alphabets used, but the evidence in nearly every case will be practically conclusive. Especially is this so if chance assists us by giving groups of three or more letters like the group CSX in the above example. The number of alphabets having been determined each alphabet is handled by the methods of Case 6 already discussed.

A later and more detailed example (Case 7-a) will demonstrate pairs that aren't separated by multiples of the number of alphabets used, but the evidence in almost every instance will be practically conclusive. This is especially true if chance helps us by providing groups of three or more letters, like the group CSX Corporation in the previous example. Once the number of alphabets is established, each alphabet is managed using the methods from Case 6 that we've already talked about.

Case 7-a.—The following message appeared in the “personal” column of a London paper:

Situation 7-a.—The following message was published in the “personal” section of a London newspaper:

“M. B. Will deposit £27 14s 5d tomorrow,”

“M. B. will deposit £27.72 tomorrow,”

and the next day we find this one: [60]

and the next day we find this one: [__A_TAG_PLACEHOLDER_0__]

M.B. CT OSB UHGI TP IPEWF H CEWIL NSTTLE FJNVX XTYLS FWKKHI BJLSI SQ VOI BKSM XMKUL SK NVPONPN GSW OL. IEAG NPSI HYJISFZ CYY NPUXQG TPRJA VXMXI AP EHVPPR TH WPPNEL. UVZUA MMYVSF KNTS ZSZ UAJPQ DLMMJXL JR RA PORTELOGJ CSULTWNI XMKUHW XGLN ELCPOWY OL. ULJTL BVJ TLBWTPZ XLD K ZISZNK OSY DL RYJUAJSSGK. TLFNS UVD VV FQGCYL FJHVSI YJL NEXV PO WTOL PYYYHSH GQBOH AGZTIQ EYFAX YPMP SQA CI XEYVXNPPAII UV TLFTWMC FU WBWXGUHIWU. AIIWG HSI YJVTI BJV XMQN SFX DQB LRTY TZ QTXLNISVZ. GIFT AII UQSJGJ OHZ XFOWFV BKAI CTWY DSWTLTTTPKFRHG IVX QCAFV TP DIIS JBF ESF JSC MCCF HNGK ESBP DJPQ NLU CTW ROSB CSM.

The messages in question appeared in an English newspaper. It is fair to presume then that the cipher is in English. This is checked negatively by the fact that it contains the letter W which is not used in any of the Latin languages and that the last fifteen words of the message consist of from two to four letters each, an impossible thing in German. It contains 108 groups which are probably words, as there are 473 letters or an average of 4.4 letters per group, while we normally expect an average of about 5 letters per group. The vowels AEIOU number 90 and the letters JKQXZ number 78. It is thus a substitution cipher (20% of 473=94.6).

The messages in question showed up in an English newspaper. It's reasonable to assume, then, that the cipher is in English. This is contradicted by the fact that it includes the letter W, which isn't used in any Latin languages, and that the last fifteen words of the message are made up of two to four letters each—something that's impossible in German. There are 108 groups that are likely words, as they total 473 letters, which averages out to 4.4 letters per group, while we generally expect about 5 letters per group. The vowels AEIOU appear 90 times, and the letters JKQXZ appear 78 times. This indicates it's a substitution cipher (20% of 473=94.6).

Recurring words and similar groups are AIIWG, AII; BKSM, BKAI; CT, CTWY, CTW; DLMMJXL, DL; ESF, ESBP; FJNVX, FJHVSI; NPSI, NPUXQG; OSB, OSY, ROSB; OL, OL; PORTELOGJ, PO; SQ, SQA; TP, TP; TLBWTPZ, TLFNS, TLFTWMC; UVZUA, UVD, UV; XMKUL, XMKUHW; YJL, YJVTI. [61]

Recurring words and similar groups are AIIWG, AI; BKSM, BKAI; CT, CTWY, CTW; DLMMJXL, DL; ESF, ESBP; FJNVX, FJHVSI; NPSI, NPUXQG; OSB (Oriented Strand Board), OSY, ROSB; OL, OL; PORTELOGJ, PO; SQ, SQA; TP, TP; TLBWTPZ, TLFNS, TLFTWMC; UVZUA, UVD, UV; XMKUL, XMKUHW; YJL, YJVTI. [__A_TAG_PLACEHOLDER_0__]

Frequency Table for the Message

A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
15	13	15	8	13	20	16	16	30	21	13	27	14	19	15	26	13	9	33	30	17	12	19	20	19	11

This clearly eliminates Cases 4, 5 and 6.

This clearly rules out Cases 4, 5, and 6.

Referring to the recurring words and groups above noted, we figure the number of letters between each.

Referring to the repeated words and groups mentioned above, we calculate the number of letters between each.

AII	...	AII	45	=	3×3×5
BK	...	BK	345	=	23×3×5
CT	...	CT	403		No factors
CTW	...	CTW	60	=	2×2×3×5
DL	...	DL	75	=	3×5×5
ES	...	ES	14	=	2×7
FJ	...	FJ	187		No factors
NP	...	NP	14	=	2×7
OL	...	OL	120	=	2×2×2×3×5
OS	...	OS	220	=	11×2×2×5
OSB	...	OSB	465	=	31×3×5
PO	...	PO	105	=	7×3×5
SQ	...	SQ	250	=	2×5×5×5
TLF	...	TLF	80	=	2×2×2×2×5
TP	...	TP	405	=	3×3×3×3×5
UV	...	UV	115	=	23×5
XMKU	...	XMKU	120	=	2×2×2×3×5
UV	...	UV	73		No factors
YJ	...	YJ	85	=	17×5

The dominant factor is clearly 5, so we may consider that five alphabets were used, indicating a keyword of five letters. Writing the message in lines of five letters each and making a frequency table for each of the five columns so formed, we find the following:

The main factor is definitely 5, so we can assume that five alphabets were used, which suggests a keyword of five letters. By writing the message in rows of five letters each and creating a frequency table for each of the five columns that result, we find the following:

Frequency Tables

Colum 1		Column 2		Column 3		Column 4		Column 5
A	11	A	111111111	A	1	A	1	A	11
B		B	111	B	111	B		B	1111111
C	1111111	C	1	C	111	C	1111	C
D	11	D	11	D	1	D		D	111
E	1111	E		E	11	E	1111111	E
F	111	F		F	111111111	F	111	F	11111
G	111111111	G		G	111	G	11	G	11
H	111	H	11111	H	111	H	111	H	11
I	11	I	11	I	1111111	I	11111111111111111	I	11
J	11111	J	1	J	111111	J		J	111111111
K	111111	K	11111	K		K	1	K	1
L		L	1111111111111111111	L	11	L	11111	L	1
M		M		M	1111111	M	1111	M	111
N	1111111	N	111	N	1111	N		N	11111
O	11111	O		O	111111111	O	1	O
P	1111111	P	1111111	P	11111111	P	1111	P
Q	11111	Q		Q		Q	11	Q	111111
R		R	1	R	1	R	111111	R	1
S		S	11111111	S	111111	S	111111111111	S	1111111
T	1111111	T	111	T	11111	T	1	T	11111111111111
U	1111111	U	111	U	111111	U		U	1
V	11111	V		V	11	V	11111	V
W	111	W	1111	W		W	11111	W	1111111
X	11	X		X	1111	X	11111111	X	111111
Y	1111	Y	11111	Y		Y	111	Y	1111111
Z		Z	11111	Z	111	Z		Z	111

In the table for Column 1, the letter G occurs 9 [62]times. Let us consider it tentatively as E. Then if the cipher alphabet runs regularly and in the direction of the regular alphabet, C (7 times) = A and the cipher alphabet bears a close resemblance to the regular frequency table. Note TUV (= RST) occurring respectively 7, 7, and 5 times and the non-occurrence of B, L, M, R, S, Z, (= Z, J, K, P, Q, and X respectively.)

In the table for Column 1, the letter G appears 9 [__A_TAG_PLACEHOLDER_0__] times. Let’s consider it tentatively as E. If the cipher alphabet runs consistently and follows the order of the regular alphabet, then C (7 times) equals A, and the cipher alphabet closely resembles the regular frequency table. Note that TUV (= RST) appears 7, 7, and 5 times respectively, while B, L, M, R, S, and Z do not appear at all (= Z, J, K, P, Q, and X respectively.)

In the next table, L occurs 19 times and taking it for E with the alphabet running in the same way, A=H. The first word of our message, CT, thus becomes AM when deciphered with these two alphabets and the first two letters of the key are C H.

In the next table, L appears 19 times, and if we treat it as E with the alphabet following the same pattern, A=H. Therefore, the first word of our message, CT, translates to AM when decoded using these two alphabets, and the first two letters of the key are C H.

Similarly in the third table we may take either F or O for E, but a casual examination shows that the former is correct and A=B (even if we were looking for a vowel for the next letter of the keyword).

Similarly, in the third table, we can use either F or O for E, but a quick look reveals that the former is correct, and A=B (even if we were searching for a vowel for the next letter of the keyword).

In the fourth table, I is clearly E and A=E. The fifth table shows T=14 and J=9. If we take T=E we find that we would have many letters which should not occur. On the other hand, if we take J=E then T=O and in view of the many E’s already accounted for in the other columns, this may be all right. It checks as correct if we apply the last three alphabets to the second word of our message, OSB, which deciphers NOW. Using these alphabets to decipher the whole message, we find it to read:

In the fourth table, I is clearly E and A=E. The fifth table shows T=14 and J=9. If we assume T=E, we'd end up with a lot of letters that shouldn't be there. On the flip side, if we take J=E, then T=O, and considering the many E’s already noted in the other columns, this might work. It checks out correctly if we apply the last three alphabets to the second word of our message, OSB (Oriented Strand Board), which decodes to NOW. Using these alphabets to decode the entire message, we find it reads:

“M. B. Am now safe on board a barge moored below Tower Bridge where no one will think of looking for me. Have good friends but little money owing to action of police. Trust, little girl, you still believe in my innocence although things seem against me. There are reasons why I should not be questioned. Shall try to embark before the mast in some outward bound vessel. Crews will not be scrutinized so sharply as passengers. There are those who will let you know my movements. Fear the police may [63]tamper with your correspondence but later on when hue and cry have died down will let you know all.”

“M. B. I’m now safe on a barge docked below Tower Bridge where no one will think to look for me. I have good friends but not much money because of the police's actions. I hope, little girl, that you still believe in my innocence even though things look bad for me. There are reasons I shouldn’t be questioned. I’ll try to sign on with a crew on a ship headed out to sea. They won’t inspect the crew as closely as the passengers. There will be people who will keep you updated on my situation. I’m worried the police might [__A_TAG_PLACEHOLDER_0__] interfere with your mail, but later, when the commotion has calmed down, I’ll let you know everything.”

The key to this message is CHBEF which is not intelligible as a word but if put into figures indicating that the 2d, 7th, 1st, 4th, and 5th letter beyond the corresponding letter of the message has been used the key becomes 27145 and we may connect it with the “personal” which appeared in the same paper the day before reading:

The key to this message is CHBEF, which doesn’t make sense as a word. However, if you use numbers to indicate that the 2nd, 7th, 1st, 4th, and 5th letters beyond the corresponding letters of the message have been used, the key becomes 27145. We can relate this to the “personal” that appeared in the same paper the day before reading:

“M. B. Will deposit £27 14s 5d tomorrow.”

“M. B. will deposit £27.72 tomorrow.”

Case 7-b.

Message

DDLRM	ERGLM	UJTLL	CHERS	LSOEE	SMEJU
ZJIMU	DAEES	DUTDB	GUGPN	RCHOB	EQEIE
OOACD	EIOOG	COLJL	PDUVM	IGIYX	QQTOT
DJCPJ	OISLY	DUASI	UPFNE	AECOB	OESHO
BETND	QXUCY	LUQOY	EHYDU	LXPEQ	FIXZE
PDCNZ	ENELQ	MJTSQ	ECFIE	ARNDN	ETSCF
IFQSE	TDDNP	UUZHQ	CDTXQ	IRMER	GLXBE
IQRXJ	FBSQD	LDSVI	XUMTB	AEQEB	YLECO
IYCUD	QTPYS	VOQBL	ULYRO	YHEFM	OYMUY
ROYMU	EQBLV	UBREY	GHYTQ	CMUBR	EQTOF
VSDDU	DAFFS	CEBSV	TIOYE	TCLQX	DVNLQ
XYTSI	MZULX	BAXQR	ECVTD	ETGOB	CCUYF
TTNXL	UNEFS	IVIJR	ZHSBY	LLTSI

On the preliminary determination, we have the following count of letters out of a total of 385:

On the preliminary decision, we have the following count of letters out of a total of 385:

A	8	L	23	J	9
E	38	N	11	Q	22
I	19	R	14	V	9
O	21	S	20	X	13
U	24	T	21	Z	6
Total	110	Total	89	Total	59
	28%		23%		15%

Every letter except K and W occurs at least six times. We may say then that it is a substitution cipher, Spanish text, and certainly not Case 4, 5 or 6. We will now analyze it for recurring pairs or groups [64]to determine, if it be Case 7, how many alphabets were used. The following is a complete list of such recurring groups and pairs with the number of letters intervening and the factors thereof. In work of this kind, the groups of three or more letters are always much more valuable than single pairs. For example, the groups, HOBE, OYMU, RMERGL and UBRE show, without question, that six alphabets were used. It is not necessary, as a rule, to make a complete list like the following:

Every letter except K and W appears at least six times. So, we can say that it’s a substitution cipher, in Spanish, and definitely not Case 4, 5, or 6. Now, we will analyze it for recurring pairs or groups [__A_TAG_PLACEHOLDER_0__] to determine, if it's Case 7, how many alphabets were used. Below is a complete list of these recurring groups and pairs along with the number of letters in between and their factors. In this kind of work, groups of three or more letters are always much more valuable than single pairs. For example, the groups HOBE, OYMU, RMERGL, and UBRE clearly indicate that six alphabets were used. Typically, it’s not necessary to create a complete list like the one below:

AE	74=2×37	IE	110=2×5×11	RE	50=2×5×5
AE	120=2×2×2×3×5	IM	302=2×151	RMERGL	198=2×3×3×11
BE	88=2×2×2×11	IO	250=2×5×5×5	SC	132=2×2×3×11
CD	132=2×2×3×11	IX	78=2×3×13	SD	262=2×131
CFI	12=2×2×3	LY	158=2×79	SI	230=2×5×23
CH	36=2×2×3×3	JT	150=2×3×5×5	SI	34=2×17
CO	42=2×3×7	LL	367 No factors	SI	264=2×2×2×3×11
CO	126=2×3×3×7	LQ	164=2×2×41	SI	12=2×2×3
CU	114=2×3×19	LQX	6=2×3	SL	78=2×3×13
DD	186=2×3×31	LU	124=2×2×31	SQ	54=2×3×3×3
DD	116=2×2×29	LU	110=2×5×11	SV	27=3×3×3
DE	285=5×57	LU	234=2×3×3×13	SV	63=3×3×7
DL	218=2×109	LX	66=2×3×11	SV	90=2×3×3×5
DN	14=2×7	LXB	132=2×2×3×11	TD	47 No factors
DQ	120=2×2×2×3×5	LY	158=2×79	TD	165=3×5×11
DU	36=2×2×3×3	ME	22=2×11	TD	96=2×2×2×2×2×3
DU	24=2×2×2×3	MU	24=2×2×2×3	TN	239 No factors
DU	38=2×19	MU	240=2×2×2×2×3×5	TS	14=2×7
DU	165=3×5×11	MU	18=2×3×3	TS	156=2×2×3×13
EA	30=2×3×5	ND	47 No factors	TSI	50=2×5×5
EB	78=2×3×13	NE	48=2×2×2×2×3	UBRE	12=2×2×3
EC	180=2×2×3×3×5	NE	18=2×3×3	UD	60=2×2×3×5
ECO	126=2×3×3×7	NE	192=2×2×2×2×2×2×3	UDA	270=2×3×3×3×5
EES	14=2×7	OB	6=2×3	UL	114=2×3×19
EF	105=3×5×7	OB	234=2×3×3×13	ULX	198=2×3×3×11
EI	8=2×2×2	OE	93=3×31	UY	89 No factors
EI	152=2×2×2×19	OI	144=2×2×2×2×3×3	UZ	162=2×3×3×3×3
EQ	88=2×2×2×11	OO	7 No factors	VI	148=2×2×37
EQ	264=2×2×2×3×11	OY	6=2×3	VT	33=3×11
EQ	44=2×2×11	OY	46=2×23	XQ	114=2×3×19
EQE	176=2×2×2×2×11	OYMU	6=2×3	XQ	144=2×2×2×2×3×3[__A_TAG_PLACEHOLDER_0__]
ER	12=2×2×3	PD	75=3×5×5	XU	99=3×3×11
ES	78=2×3×13	QBL	24=2×2×2×3	YE	184=2×2×2×23
ET	135=3×3×5	QC	95=5×19	YL	106=2×53
ET	9=3×3	QE	108=2×2×3×3×3	YL	144=2×2×2×2×3×3
ET	54=2×3×3×3	QE	68=2×2×17	YM	6=2×3
ET	31 No factors	QR	132=2×2×3×11	YRO	12=2×2×3
HE	245=5×7×7	QTO	210=2×3×5×7	ZE	6=2×3
HOBE	66=2×3×11	QX	198=2×3×3×11	ZH	183=3×61

Out of one hundred and one recurring pairs we have fifty with the factors 2×3=6; out of twelve recurring triplets, nine have these factors; and the four recurring groups of four or more letters all have these factors. The percentages are respectively 49.5%, 75% and 100% and we may be certain from this that six alphabets were used. But, before the six frequency tables are made up, there is one more point to be considered; why are there so many recurring groups which do not have six as a factor? The answer is that one or more of the alphabets is repeated in each cycle; that is, a key word of the form HAVANA has been used. If this were the key word, the second, fourth and sixth alphabets would be the same. We will see later that in this example the second and sixth alphabets are the same and this introduces the great number of recurring groups without the factor 6.

Out of one hundred and one recurring pairs, we have fifty with the factors 2×3=6; out of twelve recurring triplets, nine have these factors; and all four recurring groups of four or more letters have these factors. The percentages are 49.5%, 75%, and 100%, and we can be sure from this that six alphabets were used. However, before creating the six frequency tables, there’s one more thing to consider: why are there so many recurring groups that don’t have six as a factor? The answer is that one or more of the alphabets is repeated in each cycle; that is, a key word of the form Havana has been used. If this were the key word, the second, fourth, and sixth alphabets would be the same. We will see later that in this example, the second and sixth alphabets are the same, which leads to the large number of recurring groups without the factor of 6.

We will now proceed to make a frequency table for each alphabet. As the message is written in thirty columns, we take the first, seventh, thirteenth, etc., as constituting the first alphabet; the second, eighth, fourteenth, etc., as constituting the second alphabet and so on. The prefix and suffix letter is noted for each occurrence of each letter. The importance of this will be appreciated when the form of the frequency tables is examined. None bears any resemblance to the normal frequency table except that each is evidently a mixed up alphabet. The [66]numbers after “Prefix” and “Suffix” refer to the alphabet to which these belong, for convenience in future reference.

We will now create a frequency table for each alphabet. Since the message is arranged in thirty columns, we take the first, seventh, thirteenth, etc., to form the first alphabet; the second, eighth, fourteenth, etc., to create the second alphabet, and so on. The prefix and suffix letters are noted for each occurrence of every letter. The significance of this will become clear when we look at the frequency tables. None of them resembles the typical frequency table except that each is clearly a scrambled alphabet. The [__A_TAG_PLACEHOLDER_0__]numbers next to “Prefix” and “Suffix” indicate which alphabet they belong to for easy reference later.

Frequency Tables

First Alphabet					Second Alphabet
	Letter		Prefix (6)	Suffix (2)		Letter		Prefix (1)	Suffix (3)
A	111	3	DUD	ESF	A		0
B	11111111	8	OOOFEEOS	EOESYSCY	B	111	3	TQQ	ALL
C		0			C	1	1	B	C
D	1111	4	TYT	DJUD	D	111111	6	DTPDXT	LBCNVE
E	1	1	E	S	E	11111111111 1	1	ABNBNINRRYN	EOATLATYQTF
F		0			F	111	3	QIA	IQF
G		0			G	11	2	RR	LL
H		0			H	1	1	Z	O
I	11111111	8	EOFFEOVS	OSEFQYJ	I		0
J		0			J	1111	4	ZLDI	ILCR
L	1	1	O	J	L	1	1	T	L
M	1	1	F	O	M	1	1	V	I
N	1111	4	FEDU	EEEE	N	1	1	P	R
O	1	1	E	O	O	1111111	7	OIBQRMR	AOEYYYY
P	11	2	GE	ND	P	1	1	T	Y
Q	1111	4	UEOE	OFBB	Q	11111	5	XXITX	OIRCR
R	1111111	7	EEEYYBB	GSGOOEE	R		0
S	1	1	D	V	S	11111111	8	REIATBVB	LMLIQQDV
T	11111111	8	JUJMQYVF	LDSBPQDT	T	1	1	T	N
U		0			U	111	3	XDZ	CLL
V	11	2	UF	MS	V	1	1	S	I
X	111111	6	YQTQQA	QUQDYQ	X		0
Y	1	1	O	E	Y	1111	4	BIXB	LCTL
Z	111	3	UUM	JHU	Z		0
Third Alphabet					Fourth A is for Alphabet
	Letter		Prefix (2)	Suffix (4)		Letter		Prefix (3It seems you've sent a placeholder without any text to modernize. Please provide a phrase, and I'll help you with it!	Suffix (5)
A	1111	4	OEEB	CERE	A		0
B	1	1	D	G	B		0
C	111111	6	JUDYQC	PYNUMU	C	11111	5	LRAQT	HHDDL
D	1	1	S	D	D	11	2	QD	LU
E	111	3	EOD	SST	E	11111111	8	MQAYQALR	JICHCQCC
F	11	2	FE	SS	F		0
G		0			G	1111	4	BOIY	UCIH
H		0			H	1	1	Y	E
I	111111	6	JMSFQV	MGUXRX	I		0
J		0			J		0
L	11111111111111	14	DGLSJSUEGYBBUY	RMCSPYXQXEUVXL	L	1	1	L	T
M	1	1	S	E	M	11111	5	LIYYC	UUUUU
N	11	2	DT	PX	N	111	3	TCV	DZL
O	1	1	O	G	O		0
P		0			P	111	3	LCN	DJU
Q	1111111	7	EQSFHSE	ETESCDT	Q	1	1	L	M
R	1111	4	NQQJ	CXEZ	R	111	3	LAI	MNM
S		0			S	111111111	9	LEETQYFTF	ODHCEVCII
T	1111	4	EEEY	NSCS	T	1111	4	QQVE	OOIG
U		0			U	1111	4	ICLC	PDLY
V	11	2	SD	TN	V	1	1	L	U
X		0			X	1111111	7	LILRILN	PZBUBL
Y	111111	6	OPOOOE	ESHMMG	Y	11	2	LC	DLJ
Z		0			Z	1	1	R	H [__A_TAG_PLACEHOLDER_0__]
5th Alphabet					6th Alphabet
	Letter		Prefix (4)	Suffix (6)		Letter		Prefix (5)	Suffix (1)
A		0			A	1	1	B	X
B	11	2	XX	EA	B	11	2	UU	RR
C	1111111	7	GDDSDSD	OOFFOEV	C		0
D	111111	6	SCPYNCU	UEUUQTQ	D	1111	4	UNLU	ANSA
E	11	2	SH	TP	E	1111111111111	13	MHOIDPZZMBQUC	RREOIQPNRIBQB
F		0			F	1111111	7	PCCJEOC	NIIBMVT
G	1	1	U	T	G	1	1	U	P
H	111111	6	CCSDGZ	EOOYYS	H		0
I	11111	5	EGTSS	EYOMV	I		0
J	111	3	EPX	UOP	J	11	2	UM	TT
L	111111	6	YDUCNX	UDYQQU	L		0
M	111	3	RQR	EJE	M	11	2	UI	TZ
N	1	1	R	D	N		0
O	111	3	STT	ETF	O	111111111	9	HCJCHCVIG	BLIBBIQYB
P	11	2	UX	FE	P		0
Q	1	1	E	E	Q	1111	4	DDLL	XTXX
R		0			R		0
S		0			S	11	2	HT	BI
T	1	1	L	S	T	111	3	OED	DDX
U	1111111111	10	MMGPXMMVMD	JDGUMYEBBD	U	1111111	7	JDDDLUL	ZTVAQZN
V	1	1	S	O	V	11	2	CI	TI
X		0			X	1	0	I
Y	1	1	U	F	Y	11111	5	IHLUH	XDRRT
Z	11	2	XN	EE	Z		0

We will now set down some of the determinations which can be made at once from these frequency tables. Clearly several mixed alphabets have been used. As was to be expected from the analysis of the recurring groups, we note that the frequency tables for alphabets 2 and 6 are of so nearly the same general form that certainly these two alphabets are one and the same. If a Spanish word has been used as a key word, this means that A is probably represented by a vowel in these two alphabets and probably equals A or O, because these two letters are such common finals in Spanish.

We will now outline some conclusions that can be drawn right away from these frequency tables. It's clear that multiple mixed alphabets have been used. As we expected from analyzing the recurring groups, we observe that the frequency tables for alphabets 2 and 6 are so similar in general structure that these two alphabets must be the same. If a Spanish word has been used as a key word, this suggests that A is likely represented by a vowel in these two alphabets, probably corresponding to A or O, since these two letters are very common endings in Spanish.

1st Alphabet. Probable vowels T, X; probable common consonants, B, I, N, R. We conclude this because of the frequency of occurrence of T and X and the variety of their prefixes and suffixes. On the other hand, B, I, N, and R have for prefixes and suffixes, in a majority of cases, E, F, O and S which are the probable vowels in the 2d and 6th alphabets.

1st Alphabet. Likely vowels T, X; likely common consonants, B, I, N, R. We reach this conclusion based on how frequently T and X appear, along with the variety of their prefixes and suffixes. In contrast, B, I, N, and R mostly have prefixes and suffixes like E, F, O, and S, which are the likely vowels in the 2nd and 6th alphabets.

2d and 6th Alphabets.—Probable vowels E, F, O, S; probable common consonants, D, J, Q, U, Y. [68]

2d and 6th Alphabets.—Likely vowels E, F, O, S; likely common consonants, D, J, Q, U, Y. [__A_TAG_PLACEHOLDER_0__]

3d Alphabet.—Probable vowels C, I, L; probable common consonants A, Q, T, Y.

3d Alphabet.—Likely vowels C, I, L; likely common consonants A, Q, T, Y.

4th Alphabet.—Probable vowels, E, G, S, T; probable common consonants, C, M, N, P, U, X.

4th Alphabet.—Likely vowels, E, G, S, T; likely common consonants, C, M, N, P, U, X.

5th Alphabet.—Probable vowels, D, L, U; probable common consonants, C, H, I.

5th Alphabet.—Likely vowels, D, L, U; likely common consonants, C, H, I.

Now this cipher may have been made up from five distinct alphabets with letters chosen at random but it is much more likely to have been prepared with a cipher disk or equivalent, having the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. An equivalent form of apparatus (not using the mixed alphabet in question) is one like this:

Now this cipher might have been created using five different alphabets with letters picked at random, but it's much more likely that it was made with a cipher disk or a similar device, with the regular alphabet on the fixed disk and the mixed alphabet on the movable disk. A similar type of equipment (not using the mixed alphabet mentioned) is one like this:

Fixed Alphabet of Text
ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
	PCJVRQZBAODFSUTMXIYHLGEN
	Movable Alphabet of Cipher

Here A of the plain text is enciphered by S and the other letters come as they will. If we move the cipher alphabet one space to the left, A will be enciphered by U and the whole sequence of the alphabet will be changed.

Here A of the plain text is encrypted by S and the other letters come as they are. If we shift the cipher alphabet one space to the left, A will be encrypted by U and the entire sequence of the alphabet will change.

We will therefore use some such form as the above and see if we can insert our letters, as they are determined, in such a way as to have each of the cipher slips identical. We may start thus:

We will use a format like the one above and see if we can place our letters, as they are arranged, so that all the cipher slips are identical. We can begin like this:

	ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
1st Alphabet	t x
2d	ol qei ms d c u
3d	ol qei ms d c u
4th	ol qei ms d c u
5th	d c u ol qei ms
6th	ol qei ms d c u

In the 1st alphabet, T and X are placed as A and E respectively on the basis of frequency. In the 2d and 6th alphabets, O and E are placed as A and E respectively on the basis of frequency. In the 4th [69]alphabet, E and S are placed as A and E, and in the 5th, D, U and L are placed as A, E and O for the same reason. We now have an excess of E’s and a deficiency of A’s, which will be corrected if, in the 3d alphabet, we place L, I and C as A, E and O respectively. As a check, this gives us TOLEDO as the key word.

In the 1st alphabet, T and X are positioned as A and E respectively based on their frequency. In the 2nd and 6th alphabets, O and E are placed as A and E respectively using the same criteria. In the 4th [__A_TAG_PLACEHOLDER_0__] alphabet, E and S are set as A and E, and in the 5th, D, U, and L are assigned as A, E, and O for the same reason. We now have too many E’s and not enough A’s, which can be balanced if, in the 3rd alphabet, we designate L, I, and C as A, E, and O respectively. As a verification, this gives us Toledo as the keyword.

In the second alphabet, O is four letters to the left of E; we may place O four letters to the left of E in the fourth and it comes under V. Note that in the fourth frequency table O (= V) does not occur. In the same way in the fourth alphabet, S is four letters to the right of E; placing it in the same position with respect to E in the second and sixth, we have S under I. We have already noted that S probably represents a vowel in these two alphabets. In this way, we may add D and U to the third alphabet from their position in the fifth with respect to L and we may add I and O to the fifth from their position in the third with respect to L. In every case we check results from the frequency tables and find nothing unlikely in the results.

In the second alphabet, O is four letters to the left of E; we can place O four letters to the left of E in the fourth, and it aligns with V. Note that in the fourth frequency table, O (= V) does not appear. Similarly, in the fourth alphabet, S is four letters to the right of E; if we position it the same way with respect to E in the second and sixth, we have S under I. We've already mentioned that S likely represents a vowel in these two alphabets. This way, we can add D and U to the third alphabet based on their position in the fifth relative to L, and we can add I and O to the fifth from their position in the third relative to L. In every case, we check the results from the frequency tables and find nothing unexpected.

Now in the second and sixth, let us try Q, D and U as D, N and R respectively. We may add these letters to the third, fourth and fifth alphabets by the method of observing the number of letters to the right or left of some letter already fixed. We now add L to the second, third, fourth and sixth from its position with reference to D and U in the fifth. M is probably D in the fourth and we may add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.

Now in the second and sixth, let’s try Q, D, and U as D, N, and R respectively. We can add these letters to the third, fourth, and fifth alphabets by looking at the number of letters to the right or left of some letter that is already in place. We now add L to the second, third, fourth, and sixth based on its position in relation to D and U in the fifth. M is likely D in the fourth, and we can add it to each of the alphabets, except the first, in the same way. The table is now complete as shown.

Let us try these letters on the first line of the message and see if some other letters will be self-evident.

Let’s take these letters and put them on the first line of the message to see if any other letters will be obvious.

Alphabet

Message

Deciphered

[70]

[__A_TAG_PLACEHOLDER_0__]

Referring to our frequency tables as a check on suppositions, we find everything agrees well enough if we assume the first line to read:

Referring to our frequency tables as a check on our assumptions, we find everything aligns pretty well if we assume the first line reads:

UNAFUERZA DE CABALLERIA ENEMIGA

UNAFUERAZ DE CABALLERIA ENEMIGA

We will now put the newly found letters in the table. The letters previously found are in capitals and the new letters in small letters. The addition of D (=U) to the first alphabet permits us to add all the letters of the other alphabets to the first by the methods already discussed. Each of the other letters may then be added to every alphabet by these methods:

We will now place the newly discovered letters in the table. The letters found earlier are in uppercase, while the new letters are in lowercase. Adding D (=U) to the first alphabet allows us to include all the letters from the other alphabets to the first using the methods we've already discussed. Each of the other letters can then be added to every alphabet using these methods:

	ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
1st	T xhgoljqei msr d c u
2d	t xhgOLjQEI MSr D C U
3d	t xhgOLjQEI MSr D C U
4th	t xhgOLjQEI MSr D C U
5th	t xhgOLjQEI MSr D C U
6th	t xhgOLjQEI MSr D C U

One alphabet checks another in this way and we find everything to fit so far. We will decipher a few words more of the cipher message by the above alphabets and see if we can determine some new letters.

One alphabet verifies another like this, and we see that everything makes sense so far. We'll decode a few more words of the cipher message using the alphabets above and see if we can identify some new letters.

Alphabet

5612345612345612345612345612345612345612345612345612345612

Message

JUZJIMUDAEESDUTDBGUGPNRCHOBEQEIEOOACDEIOOGCOLJLPDUVMIGIYXQ

Deciphered

PR_CEDEN_EDEARAU__UEZ_ILLA_ECASEHA_LAENAZUCAICA_AR_HEUS_ED

Again referring to the frequency tables the first word is evidently PROCEDENTE. We have also HALLA and MARCHEUSTED. The letter B may be determined from another cipher group, JFBSQDLD (56123456) = POSICION. The letter N may be determined from BETNDQXUC (123456123) = SERRADERO. The letters F and Y may be determined from JCPJOISLYDUASIUPF (23456123456123456)= [71]COMPANIA PARTIENDO. The completed alphabets, arranged as before, are:

Again referring to the frequency tables, the first word is clearly PROCEDENT. We also have HALLA and MARCHETTED. The letter B can be identified from another cipher group, JFBSQDLD (56123456) = POSITION. The letter N can be determined from BETNDQXUC (123456123) = SERRADERO. The letters F and Y can be identified from JCPJOISLYDUASIUPF (23456123456123456)= [__A_TAG_PLACEHOLDER_0__]Company Departing. The completed alphabets, arranged as before, are:

	ABCDEFGHIJLMNOPQRSTUVXYZABCDEFGHIJLMNOPQRSTUVXYZ
1st	TYVNXHGOLJQEIZMSRBADFCPU
2d	TYVNXHGOLJQEIZMSRBADFCPU
3d	TYVNXHGOLJQEIZMSRBADFCPU
4th	TYVNXHGOLJQEIZMSRBADFCPU
5th	TYVNXHGOLJQEIZMSRBADFCPU
6th	TYVNXHGOLJQEIZMSRBADFCPU

The key word is TOLEDO and the completely deciphered message is:

The key word is TOLEDO and the fully decoded message is:

“Una fuerza de caballeria enemiga procedente de Aranjuez y Villaseca se halla en Azucaica. Marche usted con su compania partiendo de la casa de la serradero por las alturas de lo este y norte de Azucaica con el fin de reconocer su numero y clase de fuerzas y en disposicion que se halla. (Q) Esta acantonada (Q) Se hallan otras tropas detras de ella (Q). El resultado del reconocimiento necesito saberlo dentro de tres horas y media cuando mas. Pongo a sus ordenes un ciclista (X) Fin.”

“Enemy cavalry from Aranjuez and Villaseca is in Azucaica. You should march with your company starting from the sawmill house, going through the hills to the east and north of Azucaica to assess their numbers and type of forces, and their current position. (Q) They are camped (Q). There are other troops behind them (Q). I need to know the outcome of the reconnaissance within three and a half hours at the latest. I’m putting a cyclist at your disposal (X) End.”

Special Solution for Case 7

When a short message is enciphered with a long key word, the methods of analysis already discussed may fail; first, because there will be no recurring pairs to indicate the number of alphabets used and, second, because there will be so few letters in each alphabet that the methods of Case 6 will not be easily applied.

When a short message is encoded with a long keyword, the analysis methods we talked about earlier might not work; first, because there won’t be any repeating pairs to show how many alphabets were used, and second, because there will be so few letters in each alphabet that the methods from Case 6 won't be easily applied.

However, if we know or correctly assume one word, preferably a fairly long one, in the cipher text, a solution is very simple. For example, the following message is believed to refer to reënforcements and to contain that word.

However, if we know or correctly assume one word, preferably a fairly long one, in the ciphertext, finding a solution is quite simple. For example, the following message is thought to refer to reinforcements and is believed to contain that word.

YANZV	ZNLPP	KQFXI	JBPWA
NRUQP	EPLOM	CCWHM	I

[72]

[__A_TAG_PLACEHOLDER_0__]

Let us assume that REINFORCEMENTS is the first word and that it is represented by the cipher group YANZVZNLPPKQFX. We may put the test in this tabular form, using a cipher disk and a Larrabee cipher card to determine the value of A for each letter under these two systems. Any other alphabets suspected may be tried out at the same time.

Let’s assume that BACKUP is the first word and it’s represented by the cipher group YANZVZNLPPKQFX. We can display the test in a table format, using a cipher disk and a Larrabee cipher card to find the value of A for each letter under these two systems. Any other alphabets that we suspect can be tested simultaneously.

equals

then, with cipher disk, A equals

then, with cipher disk, A is

and, in Vigenere cipher, A equals

and, in Vigenère cipher, A equals

It is evident that the guess as to the appearance of the word REINFORCEMENTS was correct, that it is the first word of the message, that the cipher disk was used in preparing the cipher and that the key words are PERMANENT BODY.

It’s clear that the guess about the word Reinforcements was right, that it’s the first word of the message, that the cipher disk was used to create the cipher, and that the key words are PERMANENT BODY.

This is, of course, an especially favorable case and we will take one less favorable to show how this method can be applied.

This is, of course, a particularly advantageous case, and we will take a less favorable one to demonstrate how this method can be applied.

Two Mexican chieftains, A and B, have been communicating with the following cipher alphabet:

Two Mexican chiefs, A and B, have been using the following cipher alphabet to communicate:

Plain text	ABCDEFGHIJLMNOPQRSTUVXYZ
Cipher	PCJVRQZBAODFSUTMXIYHLGEN

This alphabet has been determined from many radio messages from A, the superior, to B, his sub-ordinate, who has a force of about 2,000 men near the border. A uses the form ORDENO QUE instead of the more familiar MANDO QUE in all his messages giving orders to B. The following message is received from A by B’s radio station (and other listening stations) and about an hour [73]later there is a good deal of noise and movement as if B’s force were breaking camp.

This alphabet has been created based on numerous radio messages from A, the boss, to B, his subordinate, who has about 2,000 men stationed near the border. A uses the phrase ORDENO QUE instead of the more common MANDO QUE in all his messages to B that give orders. The following message is received from A by B’s radio station (and other monitoring stations), and about an hour [__A_TAG_PLACEHOLDER_0__] later, there is a lot of noise and movement as if B’s force is packing up camp.

IIHAH	YDXRP	EGQGV	JJEEE	HOBGV
GJCAG	XAESA	VVXLE	IILHM	PSQAG
BDGAV	GSQAZ

This is a substitution cipher, but it is not Case 6 using the usual alphabet of the communications from A to B and, in fact, is not Case 6 at all. The recurring pairs and triplets point to a key word of ten letters and this would give us but six letters per alphabet if it is Case 7.

This is a substitution cipher, but it is not Case 6 using the usual alphabet of the communications from A to B and, in fact, is not Case 6 at all. The recurring pairs and triplets indicate a key word of ten letters, which would give us only six letters per alphabet if it is Case 7.

The preparations for a move lead us to believe that A has given an order to B and he has, in that case, probably used the expression ORDENO QUE in the message. We will try the first nine letters of the message as in the other example, first preparing a cipher disk or equivalent sliding arrangement having on it the alphabet usually used between these chieftains or A-B cipher.

The preparations for a move make us think that A has instructed B, and in that case, he likely used the phrase ORDENO QUE in the message. We'll start by trying the first nine letters of the message like in the other example, first setting up a cipher disk or a similar sliding tool that has the alphabet commonly used between these leaders or A-B cipher.

Fixed Cipher Alphabet
PCJVRQZBAODFSUTMXIYHLGENPCJVRQZBAODFSUTMXIYHLGEN
	ABCDEFGHIJLMNOPQRSTUVXYZ
	Sliding Plain Text Alphabet

A-B Cipher
If	I	equals	O	then A equals	R
	I		R		C
	H		D		X
	A		E		R
	H		N		B
	Y		O		Q

Clearly there is nothing here and the assumed words, if they occur, are in the middle of the message. We may jump to the combination PEGQGV at once since the preceding letters do not make ORDENO QUE. We try this without result and proceed to EGQGVJ, GQGVJJ, QGVJJE, GVJJEE, [74]VJJEEE, JJEEEH, JEEEHO, EEEHOB, EEHOBG, EHOBGV, HOBGVG, OBGVGJ, BGVGJC, GVGJCA, VGJCAG, all without result. This work requires less time than might be imagined and is the kind of work which can be divided among a number of operators. Now let us come to the next combination GJCAGX. We add the next three letters, AES, against QUE.

Clearly, there's nothing here, and the assumed words, if present, are in the middle of the message. We can jump straight to the combination PEGQGV since the preceding letters don't form I ORDER THAT. We try this without any results and move on to EGQGVJ, GQGVJJ, QGVJJE, GVJJEE, [__A_TAG_PLACEHOLDER_0__]VJJEEE, JJEEEH, JEEEHO, EEEHOB, EEHOBG, EHOBGV, HOBGVG, OBGVGJ, BGVGJC, GVGJCA, VGJCAG, all without any results. This work takes less time than one might think and is the type of task that can be divided among several operators. Now let's move on to the next combination GJCAGX. We add the next three letters, AES, against QUE.

equals

Then, in the A-B cipher, A equals

The key is found; VIVA_ADERO and a trial of M in the blank space shows correct results. This checks with our theory that a ten letter key word was used and deciphering the message we have:

The key is found; VIVA_ADERO and a test of M in the empty space gives correct results. This confirms our theory that a ten-letter keyword was used, and by decoding the message, we have:

PARA EL ATAQUE CONTRA TORREON ORDENO QUE SUS TROPAS MARCHEN ESTE NOCHE X.

PARA EL ATAQUE CONTRA TORREON, ORDENE QUE SUS TROPAS MARCHEN ESTA NOCHE X.

The reason for breaking camp is now evident.

The reason for packing up the camp is now clear.

This method may be used, with some labor, on short words like THE, AND, etc. Parts of the key will appear whenever an assumed word is found in the message and the whole key may be assembled if enough of the parts are available. Even if only part of the key may be so recovered, it will always lead to the ultimate solution of the cipher by trial of the partially recovered key on the message letter by letter.

This method can be used, with some effort, on short words like THE, AND, etc. Parts of the key will show up whenever a guessed word is found in the message, and the entire key can be put together if there are enough parts available. Even if only part of the key can be recovered this way, it will still lead to the final solution of the cipher by testing the partially recovered key on the message one letter at a time.

As an example of recovery of a key by use of short common words, let us refer to the message of Case 7-a. There are twenty-four groups of three letters each in this message and we will try them against THE, ARE and YOU, assuming that the Vigenere cipher is used. [75]

As an example of retrieving a key by using simple common words, let's refer to the message of Case 7-a. There are twenty-four groups of three letters each in this message, and we'll test them against THE, ARE, and YOU, assuming that the Vigenere cipher is used. [__A_TAG_PLACEHOLDER_0__]

OSB

VOI

GSW

CYY

ZSZ

BVJ

XLD

OSY

UVD

YJL

SQA

HSI

equals

THE

ARE

YOU

then A equals

VLX

CHE

NLS

JRU

GLV

IOF

EEZ

VLU

BOZ

FCH

ZJW

OLE

OBX

VXE

GBS

CHU

ZBV

BEF

XUZ

OBU

UEZ

YSH

SZW

HBE

QEH

XAO

IEC

EKE

BEF

DHP

ZXJ

QEE

WHJ

AVR

UCG

JEO

BJV

SFX

DQB

AII

OHZ

IVX

JBF

ESF

JSC

NLU

CTW

CSM

equals

THE

ARE

YOU

then A equals

ICR

ZYT

KJX

HBE

VAV

POT

QUB

LLB

QLY

UEQ

JMS

JLI

BSR

SOT

DZX

ARE

OQV

IET

JKB

EBB

JBY

NUQ

CCS

CBI

DVB

URD

FCH

YUO

QTF

KHD

LNL

GEL

LEI

PXA

EFC

EES

In column 5, we have, for YOU, the key BEF; column 6 gives the same key for ARE; column 10 gives the key FCH for THE and column 15 gives the same key for YOU; column 12 gives the key HBE for ARE and column 16 gives the same key for THE; column 23 gives the key EFC for YOU. The only possible key for the message is a five-letter one made up of the letters BEFCH or EFCHB or FCHBE or CHBEF or HBEFC. If the key in this case were a word, we would have no difficulty in determining it; as it is, there is no real difficulty in the matter as we may now divide the message into blocks of five letters and note that ZSZ (= YOU) form the 3d, 4th and 5th letters of a group. The corresponding key letters, BEF, are then the 3d, 4th and 5th letters of the key which must be CHBEF.

In column 5, for YOU, we have the key BEF; column 6 shows the same key for ARE; column 10 provides the key FCH for THE and column 15 has the same key for YOU; column 12 gives the key HBE for ARE and column 16 shares the same key for THE; column 23 lists the key EFC for YOU. The only possible key for the message is a five-letter combination made up of the letters BEFCH or EFCHB or FCHBE or CHBEF or HBEFC. If the key were a word, identifying it would be straightforward; as it stands, we can break the message into blocks of five letters and see that ZSZ (= YOU) are the 3rd, 4th, and 5th letters of a group. The corresponding key letters, BEF, are therefore the 3rd, 4th, and 5th letters of the key, which must be CHBEF.

This special solution for Case 7 depends so largely on the intuition of the operator in choice of a word that it is not, in general, advisable to use it unless the message is very short and the regular methods of analysis have been tried unsuccessfully. It is, however, a wonderfully short cut in difficult cases where the other methods fail. [76]

This special solution for Case 7 relies heavily on the operator’s intuition when choosing a word, so it’s usually not recommended unless the message is very short and standard analytical methods have been attempted without success. However, it’s an incredibly efficient shortcut in tough situations where other methods don't work. [__A_TAG_PLACEHOLDER_0__]

1 The method used is not the most satisfactory one for several reasons and a better method is that of writing the message in multiples of the key and enciphering the columns as already described. ↑

1 The method used isn’t the best for a few reasons, and a better approach is to write the message in multiples of the key and encode the columns as described earlier. ↑

Chapter VIII

Case 8. The Playfair cipher. This is the English military field cipher; as the method is published in English military manuals and as it is a cipher of proven reliability, it may be met with in general cipher work. The Playfair cipher operates with a key word; two letters are substituted for each two letters of the text.

Case 8. The Playfair cipher. This is the English military field cipher; since the method is published in English military manuals and is a cipher of proven reliability, it may be encountered in general cipher work. The Playfair cipher uses a keyword; two letters are substituted for each pair of letters in the text.

The Playfair cipher may be recognized by the following points: (a) It is a substitution cipher, (b) it always contains an even number of letters, (c) when the cipher is divided into groups of two letters each, no group consists of the repetition of the same letter as SS or BB, (d) there will be recurrence of pairs throughout the message, following in a general way, the frequency table of digraphs of pairs, (e) in short messages there may be recurrence of cipher groups representing words or even phrases, and these will always be found in long messages.

The Playfair cipher can be identified by the following points: (a) It is a substitution cipher, (b) it always has an even number of letters, (c) when the cipher is split into groups of two letters each, no group can have the same letter repeating, like SS or BB, (d) there will be repetitions of pairs throughout the message, generally following the frequency table of digraphs, (e) in short messages, you might see repeated cipher groups that stand for words or even phrases, and these will always appear in longer messages.

In preparing a cipher by this method, a key word is chosen by the correspondents. A large square, divided into twenty-five smaller squares, is constructed as shown below and the letters of the key word are written in, beginning at the upper left hand corner. If any letter recurs in the key word, it is only used on the first occurrence. The remaining letters of the alphabet are used to fill up the square. It is customary to consider I and J as one letter in this cipher and they are written together in the same square.

In creating a cipher using this method, the correspondents choose a key word. A large square, divided into twenty-five smaller squares, is made as shown below, and the letters of the key word are filled in, starting from the upper left corner. If a letter appears more than once in the key word, it’s only included the first time. The leftover letters of the alphabet are used to complete the square. It’s common to treat I and J as one letter in this cipher, and they are combined in the same square.

If the key word chosen is LEAVENWORTH, then the square would be constructed as follows: [77]

If the chosen keyword is LEAVENWORTH, then the square would be built like this: [__A_TAG_PLACEHOLDER_0__]

L	E	A	V	N
W	O	R	T	H
B	C	D	F	G
IJ	K	M	P	Q
S	U	X	Y	Z

The text of the message to be sent is then divided up into groups of two letters each, and equivalents are found for each pair.

The message is then broken down into groups of two letters, and equivalents are identified for each pair.

Every pair of letters in the square must be: Either (1) in the same vertical line. Thus in the above example each letter is represented in cipher by that which stands next below it, and the bottom letter by the top one of the same column; for instance, TY is represented by FV.

Every pair of letters in the square must be: Either (1) in the same vertical line. So in the example above, each letter is represented in code by the one directly below it, and the bottom letter by the top one in the same column; for instance, Thanks! is represented by FV.

Or (2) in the same horizontal line. Each letter in this case is represented by that which stands next on its right, and the letter on the extreme right by that on the extreme left of the same horizontal line with it; for instance RH is represented by TW.

Or (2) in the same horizontal line. Each letter in this case is represented by the one immediately to its right, and the letter on the far right is represented by the letter on the far left of the same horizontal line; for example, RH is represented by TW.

Or (3) at opposite corners of a rectangle. Each letter of the pair is represented by the letter in the other corner of the rectangle in the same horizontal line with it; for instance TS is represented by WY.

If, on dividing the letters of the text into pairs, it is found that a pair consists of the same letter repeated, a dummy letter, as X, Y, or Z, should be introduced to separate the similar letters.

If, when splitting the letters of the text into pairs, you find that a pair has the same letter repeated, you should insert a dummy letter, like X, Y, or Z, to separate the identical letters.

If the message to be sent were “The enemy moves at dawn,” it would be divided into pairs:

If the message to be sent was “The enemy moves at dawn,” it would be split into pairs:

	TH	EX	EN	EM	YM	OV	ES	AT	DA	WN
and enciphered:	HW	AU	AL	AK	XP	TE	LU	VR	MR	HL

The message is then broken up into groups of five letters for transmission.

The message is then divided into groups of five letters for sending.

To decipher such a cryptogram, (knowing the key word), the receiver divides it into pairs, and [78]from his table finds the equivalent of these pairs, taking the letter immediately above each, when they are in the same vertical line; those immediately on the left, when in the same horizontal line; and those at opposite angles of the rectangle when this is formed.

To decode a cryptogram (using the key word), the person receiving it breaks it into pairs and [__A_TAG_PLACEHOLDER_0__]looks up their equivalents in his table. He takes the letter directly above each one when they’re in the same vertical line, those directly to the left when they're in the same horizontal line, and those at opposite corners of the rectangle when it’s formed.

It is evident, from the foregoing description, that any letter of the plain text may be represented in cipher by one of five letters, viz: The one next below it and the other four letters in the same horizontal line with it in the square. Take, for example, the letter D of the plain text, in combination with each of the other letters of the alphabet. We have, using the key LEAVENWORTH:

It’s clear from the description above that any letter from the plain text can be represented in code by one of five letters: the one directly below it and the other four letters in the same horizontal line in the square. For example, take the letter D from the plain text, combined with each of the other letters in the alphabet. Using the key LEAVENWORTH, we have:

This gives D represented by	B	C	F	G	M
	4	4	8	4	4	times,

and, connected with these five letters representing D,
we have	A	R	D	M	X	B	C	G
	5	5	2	4	5	1	1	1	times.

Note that these letters are those of the vertical column containing D plus the letters B, C and G, of the horizontal line containing D.

Note that these letters come from the vertical column that has D, along with the letters B, C, and G from the horizontal line that contains D.

Lieut. Frank Moorman, U. S. Army, has developed a method for determining the letters which make up the key word in a Playfair cipher. In the first place, a key word necessarily contains vowels in the approximate proportion of two vowels to three consonants and it is also likely that a key word will contain other common letters. This key word is placed in the first row or rows. Now if a table is made, showing what letters in the cipher occur with every letter, it will be found that the letters having the greatest number of other letters in combination with them are very likely to be letters of the key [79]word, or in other words, letters occurring in the first or second lines. An example will make this clear:

Lieut. Frank Moorman, U.S. Army, has created a method for figuring out the letters that make up the key word in a Playfair cipher. First, a key word usually contains vowels in about a two-to-three ratio with consonants, and it’s also likely that a key word will include other common letters. This key word is placed in the first row or rows. If you create a table showing which letters in the cipher appear with each letter, you’ll find that the letters with the highest number of combinations are very likely to be the letters of the key [__A_TAG_PLACEHOLDER_0__]word, meaning they probably appear in the first or second lines. An example will clarify this:

Message

Message

DB FN EX TZ MF TO VB QB QT OB XA OF PR TZ EQ RH QK QV DX OK AB PR QI EL TV KE EX XS FS BP WD BO BY BF RO EA BO RH QK QV TX GU EL AB TH TR XN ON EA AY XH BO HN EX BS HR QB ZM SE XP HF GZ UG KC BD PO EA AY XH BO XP HF KR QI AB PR QI EL BX FZ BI SE FX PB RA PR QI WC BR XD YG TB QT EA AY XH BO HN EX BS HR QB PR QI EL BX BT HB QB NF SI SE BX NU XP BU RB XB QR OX BA TB RH BP WD RP RO GU GX QR SE ZY OX BA EL AX CW BY BA SX RK RO PR HB OP BD PI CN OX EM RP KR XT EL AX CW EQ FZ SX EL RH RO PR HB UX DA SE XN ZN GU EL BX FS DG DB TB ZL VE RH BO RQ.

From this message, we make up the following table, considering the letters of each pair: [80]

From this message, we create the following table, considering the letters of each pair: [__A_TAG_PLACEHOLDER_0__]

First Letters of Pairs

First Letters of Pairs

	A	B	C	D	E	F	G	H	I	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
A		3		1	4												1						1
B	3			2				3						1	1	4	1		3		1		1
C										1												1
D		2																				2	1
E										1								5			1
F		1						2				1	1	1
G				1													1			1				1
H																	5		1				3
I		1													1	5		1
K														1		2	1
L					8																				1
M					1																				1
N			1			1		2						1									2		1
O		6													1		4		1
P		2												1			2						3
Q					2
R		1						2		2					7	2			1
S		2				2																	1
T		1														2							1
U		1					3						1
V																2
W			2
X	1	5		1	4	1	1							3				2	1	1
Y		5																							1
Z						2	1												2

From this table we pick out the letters B, E, F, O, R, T, X, as tentative letters of the key word on account of the variety of other letters with which they occur. As there are but two vowels for seven letters, we will add A to the list on account of its occurrences with B, D, E, R, and X. This leaves the letters for the bottom lines of the square as follows: [81]

From this table, we pick out the letters B, E, F, O, R, T, and X as possible letters for the key word because of the variety of other letters they appear with. Since there are only two vowels among seven letters, we'll add A to the list based on its occurrence with B, D, E, R, and X. This leaves the letters for the bottom lines of the square as follows: [__A_TAG_PLACEHOLDER_0__]

.	.	.	.	.
.	.	.	C	D
G	H	IJ	K	L
M	N	P	Q	S
U	V	W	Y	Z

Referring to the table again we find the most frequent combination to be EL, occurring 8 times, with no occurrence of LE. Now, TH is the commonest pair in plain text, and HT is not common. The fact that H occurs in the same horizontal line with L and that E and T are probably in the key, will lead us to put E in the first line over H and T in the first line over L, so as to make EL equal TH.

Referring to the table again, we find that the most common combination is EL, which occurs 8 times, while LE doesn’t appear at all. Now, TH is the most frequent pair in plain text, and HT is not common. The fact that H is in the same horizontal line as L and that E and T are likely part of the key will lead us to place E in the first line above H and T in the first line above L, so that EL equals TH.

The next most frequent combination is PR occurring 7 times, with RP occurring twice. In the square as partially arranged, PR equals M_ or N_ or Q_ or I_. We may eliminate all these except N_, and this N_ could only be NO or NA, so that we will put, tentatively the R in the second line over H and the O and A in the same line over IJ. We have then:

The next most common combination is Public Relations appearing 7 times, with RP showing up twice. In the partially arranged square, PR corresponds to M_, N_, Q_, or I. We can eliminate all of these except N_, which could only be NO or NA. Thus, we will tentatively place the R in the second line over H, and the O and A in the same line over IJ. We have then:

.	E	.	.	T
.	R	AO	C	D
G	H	IJ	K	L
M	N	P	Q	S
U	V	W	Y	Z

Let us now check this by picking out the combinations beginning with EL and seeing if the table will solve them. We find, ELTV, ELAB, ELBXFZ, ELBXBT, ELAXCWBY, ELAXCWEQ, ELRH, ELBXFS. Now, on the assumption that the letter after EL represents E, we have it represented by A three times, B three times, R once and T once. This requires [82]that A and B be put in the same horizontal line with E, since T is already there, and R is tentatively under E.

Let’s check this by picking out the combinations that start with EL and see if the table can solve them. We find ELTV, ELAB, ELBXFZ, ELBXBT, ELAXCWBY, ELAXCWEQ, ELRH, and ELBXFS. Assuming the letter after EL stands for E, we see it represented by A three times, B three times, R once, and T once. This means [__A_TAG_PLACEHOLDER_0__] that A and B should be aligned on the same horizontal line as E, since T is already there and R is tentatively under E.

The combination ELTV now equals THEZ. If the T were moved one place to the left, it would be THEY, a more likely combination, but this requires the L to be moved one place to the left also, by putting I or K in the key word and taking out O, R or X and returning it to its place in the alphabetical sequence. The most frequent pairs containing O are B O six times, R O four times, and O X three times. Now these pairs equal respectively E N, E S and H E, if O is put between N and P in the fourth line. We will therefore cease to consider it as a letter of the the key word. The combination ELAB can only be THE_ on the assumption that A is the first letter to the right of E. The combination ELBX occurs three times. If it represents THE_, the B must be the first letter of the first line and the X must now be placed under E where the R was tentatively put. We can get THE_ out of ELRH by putting R in the first line or leaving it where it is, but the preponderance of the BX combination should suggest the former alternative.

The combination ELTV now equals THEZ. If the T were moved one position to the left, it would be THEY, which is a more likely combination, but this also requires the L to be moved one position to the left by adding I or K in the keyword and removing O, R, or X and returning it to its place in the alphabetical order. The most common pairs containing O are B O six times, R O four times, and O X three times. These pairs now represent E N, E S, and H E, respectively, if O is placed between N and P in the fourth line. Therefore, we will stop considering it as a letter of the keyword. The combination ELAB can only be THE if A is the first letter to the right of E. The combination ELBX appears three times. If it represents THE, then the B must be the first letter of the first line and the X must now be placed under E, where the R was tentatively placed. We can get THE_ from ELRH by putting R in the first line or leaving it where it is, but the prevalence of the BX combination should suggest the former option.

A new square showing these changes will look like this:

A new square displaying these changes will look like this:

B	E	A	T	R
.	X	.	.	.
G	H	.	L	M
N	O	P	Q	S
U	V	W	Y	X

As I put in the space under B will give the word BEATRIX and as a vowel is clearly necessary there, we will so use the IJ and leave K between H and L. This leaves C, D and F to be placed. It appeared at [83]first that F was in the key but if it is in the second line, in proximity to the letters of the first line, it will give the same indications. Completing the square then, we have

As I fill in the space under B, it will form the word BEATRIX, and since a vowel is clearly needed there, we will use IJ and leave K between H and L. This leaves C, D, and F to be placed. It first appeared at [__A_TAG_PLACEHOLDER_0__] that F was in the key, but if it's on the second line, near the letters of the first line, it will show the same indications. Completing the square then, we have

B	E	A	T	R
IJ	X	C	D	F
G	H	K	L	M
N	O	P	Q	S
U	V	W	Y	Z

With this square, the message is deciphered without difficulty.

With this square, the message is easily understood.

“It is very frequently neces(x)sary to employ ciphers and they have for many centuries been employed in the relations betwe(x)en governments, for com(x)munication betwe(x)en com(x)manders and their subordinates and particularly betwe(x)en governments and their agents in foreign countries; there are many cases in history where the capture of a message not in cipher has made the captors of the message victorious in their military movements.”

“It is often necessary to use ciphers, and they have been used for many centuries in communications between governments, for messages between commanders and their subordinates, and especially between governments and their agents in foreign countries. There are many historical instances where intercepting a message that wasn't in code has led to victory in military operations for those who captured it.”

It will be seen that the method of Lieut. Moorman enabled us to pick out six letters of the key word out of eight letters chosen tentatively. The reason for the appearance of F has already been noted; the letter O occurred with many other letters because it happened to remain in the same line with N and S and to be under H. It thus was likely to represent any of these three letters which occur very frequently in any text.

It will be evident that Lieutenant Moorman's method allowed us to identify six letters of the keyword from eight letters we tentatively selected. The reason for the appearance of F has already been mentioned; the letter O appeared with many other letters because it happened to be in the same line as N and S and located under H. Therefore, it was likely to represent any of these three letters, which are very common in any text.

Two-character Substitution Ciphers

Case 9.—Two-character substitution ciphers. In ciphers of this type, two letters, numerals, or conventional signs, are substituted for each letter of the text. There are many ways of obtaining the characters [84]to be substituted but, in general, these ciphers may be considered as special varieties of Case 6 or Case 7. The ciphers which come under this case are not well suited to telegraphic correspondence because the cipher message will contain twice as many letters as the plain text. However they are so used; an example is at hand in which two numerals are substituted for each letter and this makes transmission by telegraph very slow.

Case 9.—Two-character substitution ciphers. In these ciphers, two letters, numbers, or symbols are swapped in for each letter in the text. There are various methods to generate the characters [__A_TAG_PLACEHOLDER_0__] that will be replaced, but generally, these ciphers can be seen as specific versions of Case 6 or Case 7. The ciphers under this category aren’t ideal for telegram communication since the cipher message contains twice as many characters as the original text. However, they are still used; for example, there’s a case where two numbers are used for each letter, which makes sending it via telegraph quite slow.

Case 9 can be recognized by some or all of the following points; the number of characters in the cipher is always an even number; often only a few, say five to ten, of the letters of the alphabet appear; either a frequency table for pairs of the cipher text resembling the normal single letter frequency table can be made, or groups of four letters will show a regular recurrence, from which the cipher can be solved as in Case 7.

Case 9 can be identified by some or all of these points: the number of characters in the cipher is always even; often only a few letters, maybe five to ten, of the alphabet are used; either a frequency table for pairs of the cipher text that resembles the typical single-letter frequency table can be created, or groups of four letters will show a consistent pattern, allowing the cipher to be solved similarly to Case 7.

Case 9a.—

Message

RNTGN RAAGR NARNA GTGRA TGAAN NANGG RARAT NAANR NNNRN AAAGG AANGR NGGNN NRNAA AANRA TNANN NGGRN RNNRG TTGRG TGGRN ARNTG NNART GGRNR GRNNT GTGAA NNARN ARNRT TGAGG GAAAA NANNA RNAGA NGNAT NNNAT

This message contains 160 letters and it will be noted that the only letters used are A, G, N, R and T.

This message has 160 letters, and it's worth noting that the only letters used are A, G, N, R, and T.

We may expect a simple two-letter substitution cipher at once. It will simplify the work if we divide the cipher into groups of two letters and then, if we find there are 26 or less recurring groups, to assign an arbitrary letter to each group and work out the cipher by the method of Case 6.

We can immediately anticipate a straightforward two-letter substitution cipher. It will make things easier if we break the cipher into pairs of letters and if we discover that there are 26 or fewer repeating pairs, we can assign a random letter to each pair and decode the cipher using the method from Case 6.

RN TG NR AA GR NA RN AG TG RA TG AA NN AN GG RA RA TN AA NR NN NR NA AA GG AA NG RN GG NN NR NA AA AN RA TN AN NN GG RN RN NR GT TG RG TG GR NA RN TG NN AR TG GR NR GR NN TG TG AA NN AR NA RN RT TG AG GG AA AA NA NN AR NA GA NG NA TN NN AT

[85]

[__A_TAG_PLACEHOLDER_0__]

With arbitrary letters substituted, we have

With random letters replaced, we have

A B C D E F A G B H B D I J K H H L D C I C F D K D M A K I C F D J H L J I K A A C N B O B E F A B I P B E C E B B D I P F A Q B G K D D F I P F R M F L I S

Now, preparing a frequency table, with note of prefixes and suffixes we have:

Now, creating a frequency table, along with notes on prefixes and suffixes, we have:

	Frequency		Prefix	Suffix
A	7	1111111	FMKAFF	BGKACBQ
B	10	1111111111	AGHNOAPIBQ	CHDOEIEBDG
C	6	111111	BDIIAE	DIFFNE
D	9	111111111	CBLFKFBKD	EICKMJIDF
E	4	1111	DBBC	FFCI
F	8	11111111	ECCEPDPM	ADDAAIRL
G	2	11	AB	BK
H	4	1111	BKJH	BHLL
I	9	111111111	DCKJBEDFL	JCCKPBPP
J	3	111	IDL	KHI
K	5	11111	JDAIG	HDIAD
L	3	111	HHF	DJI
M	2	11	DR	AF
N	1	1	C	B
O	1	1	B	B
P	3	111	III	BFF
Q	1	1	A	B
R	1	1	F	M
S	1	1	I

A brief study of this table and the distribution in the cipher leads to the conclusion that B, F and C are certainly vowels and are, if the normal frequency holds, equal to E, O, and A or I. Similarly D and I are consonants and we may take them as N and T. I is taken as T because of the combination IP (=possibly TH) occurring three times. The next letter in order of frequency is A; it is certainly a consonant and may be taken as R on the basis of its frequency. Let us now try these assumptions on the first two lines of the message. We have

A quick look at this table and the distribution in the cipher suggests that B, F, and C are definitely vowels and, assuming the usual frequencies hold, are equivalent to E, O, and A or I. Similarly, D and I are consonants, which we can consider as N and T. I is assumed to be T because the combination IP (likely representing TH) appears three times. The next letter based on frequency is A; it’s definitely a consonant and can be interpreted as R based on how often it appears. Now let’s apply these assumptions to the first two lines of the message. We have

This is clearly the word REINFORCEMENTS and, using the letters thus found, the rest of the line becomes AMMUNITIONAND. We have then the following letters determined:

This is clearly the word Reinforcements, and using the letters found, the rest of the line becomes AMMUNITION AND. We now have the following letters determined:

Arbitrary letters

Plain Text

[86]

[__A_TAG_PLACEHOLDER_0__]

If these be substituted we have for the message:

If we replace these, we get the message:

REINFORCEMENTS AMMUNITION AND RATIONS MUST ARRI_E _EFORE T_E FIFTEENT_ OR _E CANNOT _O_D OUT_.

Reinforcements, ammo, and supplies need to arrive before the fifteenth, or we won’t be able to load out.

From this the remainder of the letters are determined:

From this, the rest of the letters are determined:

Arbitrary letters	N	O	P	Q	R	S
Plain text	V	B	H	W	L	X

Now let us substitute the two-letter groups for the arbitrary letters:

Now let's replace the two-letter groups with the arbitrary letters:

Arbitrary letters

Two-letter groups

Plain text

It is evident that the cipher was prepared with the letters of the word GRANT chosen by means of a square of this kind:

It’s clear that the code was created using the letters from the word GRANT, selected through a square like this:

	G	R	A	N	T
G	A	B	C	D	E
R	F	G	H	I	K
A	L	M	N	O	P
N	Q	R	S	T	U
T	V	W	X	Y	Z

Thus TG=E, AN=S, etc., as we have already found.

Case 9-b

Message

1950492958	3123252815	4418452815	2048115041
2252115345	5849134124	5028552526	5933195222
5245113215	6215584143	2861361265	2945565015
2342455850	6345542019	1550185311	2115415828
1124174553	4554205950	2552454132	1533492048
5018152364

An examination of the groups of two numerals each which make up this message, shows that we have 11 to 36 and 41 to 65 with eleven groups missing. Now the 11 to 36 combination is a very familiar one in numeral substitution ciphers (See Case 6-c) and it [87]will be noted that 41 to 66 would give us a similar alphabet. Let us make a frequency table in this form:

An analysis of the pairs of two digits that compose this message reveals that we have numbers from 11 to 36 and 41 to 65, with eleven pairs missing. The combination from 11 to 36 is quite common in numeral substitution ciphers (See Case 6-c), and it [__A_TAG_PLACEHOLDER_0__] should be noted that 41 to 66 would provide a similar alphabet. Let’s create a frequency table in this format:

Group	Frequency	Group	Frequency
11	11111	41	11111
12	1	42	1
13	1	43	1
14		44	1
15	111111111	45	111111111
16		46
17	1	47
18	111	48	11
19	111	49	111
20	1111	50	11111111
21	1	51
22	11	52	1111
23	111	53	111
24	11	54	11
25	111	55	1
26	1	56	1
27		57
28	11111	58	11111
29	11	59	11
30		60
31	1	61	1
32	11	62	1
33	11	63	1
34		64	1
35		65	1
36	1	66

Each of these tables looks like the normal frequency table except for the position of 20 and 50 which should represent T, by all our rules, and should be apparently 30 and 60. But suppose we put the alphabet and corresponding numerals in this form:

Each of these tables looks like the usual frequency table, except for the positions of 20 and 50, which should represent T according to all our rules, and should actually be 30 and 60. But let’s say we arrange the alphabet and corresponding numbers like this:

	1	2	3	4	5	6	7	8	9	0
1 or 4	A	B	C	D	E	F	G	H	I	J
2 or 5	K	L	M	N	O	P	Q	R	S	T
3 or 6	U	V	W	X	Y	Z

[88]

[__A_TAG_PLACEHOLDER_0__]

Then A=11 or 41, J=10 or 40 and T=20 or 50 as we found. Using the above alphabet, the message may easily be read. Note that this cipher is made up of ten characters only, the Arabic numerals.

Then A=11 or 41, J=10 or 40 and T=20 or 50 as we found. Using the above alphabet, the message can easily be read. Note that this cipher consists of only ten characters, which are the Arabic numerals.

Case 9c—

Message

Message

1156254676	2542294432	1949294015	1423217211	2979703115
4924213511	7424147875	7646252444	5143254845	3179742533
4055461512	7573227945	1627481511	7042351944	1378252149
2514764553	1548342126	7215254075	1611257845	4642217415
4952197929	7015242143	2925444933	1970187531	4079254829
4551491411	7321171554

An examination of this message shows it to consist of forty-four different two-figure groups running from 11 to 79. Let us prepare a frequency table of these groups.

An analysis of this message reveals that it contains forty-four unique two-digit groups ranging from 11 to 79. Let's create a frequency table for these groups.

Group	Frequency
11	111111
12	1
13	1
14	1111
15	111111111
16	11
17	1
18	1
19	1111
20
21	1111111
22	1
23	1
24	1111
25	11111111111
26	1
27	1
28
29	111111
30
31	111
32	1
33	11
34	1
35	11
36
37
38
39
40	1111
41
42	111
43	11
44	1111
45	11111
46	1111
47
48	1111
49	111111
50
51	11
52	1
53	1
54	1
55	1
56	1
57
58
59
70	1111
71
72	11
73	11
74	111
75	1111
76	111
77
78	111
79	11111

We at once note the resemblance between the frequency tables for the groups 11 to 19 and 21 to [89]29; for the groups 30 to 36 and 50 to 56; and for the groups 40 to 49 and 70 to 79. Also the groups 11 to 19 and 21 to 29 have a frequency fitting well with the normal frequency table of the letters A to I; the groups 41 to 49 and 71 to 79 have a frequency fitting well with the normal frequency table of the letters K to S; and the groups 31 to 36 and 51 to 56 have a frequency fitting well with the normal frequency table of the letters U to Z. We have J and T unaccounted for, but note what occurred in Case 9-b and that 40 and 70 would correspond well with T if they followed respectively 49 and 79. We may now make up a cipher table as follows:

We immediately notice the similarity between the frequency tables for the groups 11 to 19 and 21 to [__A_TAG_PLACEHOLDER_0__]29; for the groups 30 to 36 and 50 to 56; and for the groups 40 to 49 and 70 to 79. Additionally, the groups 11 to 19 and 21 to 29 have a frequency that aligns well with the normal frequency table of the letters A to I; the groups 41 to 49 and 71 to 79 correspond well with the normal frequency table of the letters K to S; and the groups 31 to 36 and 51 to 56 match well with the normal frequency table of the letters U to Z. We still have J and T unaccounted for, but let's recall what happened in Case 9-b, and 40 and 70 would fit nicely with T if they followed 49 and 79 respectively. We can now create a cipher table as followsUnderstood. Please provide the text you would like me to modernize.

	1	2	3	4	5	6	7	8	9	0
1 or 2	A	B	C	D	E	F	G	H	I	J
4 or 7	K	L	M	N	O	P	Q	R	S	T
3 or 5	U	V	W	X	Y	Z

and this table will solve the cipher message.

and this table will decode the cipher message.

In ciphers coming under case 9-b and 9-c, it is not uncommon to assign some of the unused numbers such as 85, 93, etc., to whole words in common use or to names of persons or places. In case such groups are found, the meaning must be guessed at from the context; but if many messages in the same cipher are available, the meaning of these groups will soon be obtained. The appearance of such odd groups of figures in a message does not interfere materially with the analysis, and it will be apparent at once on deciphering the message that they represent whole words instead of letters. [90]

In ciphers that fall under cases 9-b and 9-c, it’s common to assign some of the unused numbers like 85, 93, etc., to whole words that are frequently used or to names of people or places. When such groups are encountered, their meanings must be inferred from the context; however, if there are multiple messages in the same cipher, the meanings of these groups will quickly become clear. The presence of these unusual groups of numbers in a message doesn't significantly hinder the analysis, and it will be obvious right away when deciphering the message that they stand for whole words rather than individual letters. [__A_TAG_PLACEHOLDER_0__]

Chapter IX

Other Substitution Methods

The foregoing cases by no means exhaust the possibilities of the substitution cipher but they cover practically all methods which are satisfactory for military purposes, having in mind conservation of time, the minimizing of mental strain, and the requirements that complicated apparatus and rules be avoided, and that the resulting cipher should be adapted to telegraphic correspondence.

The cases discussed above definitely don’t cover all the possibilities of the substitution cipher, but they include almost all the methods that work well for military use, focusing on saving time, reducing mental effort, and the need to avoid complicated equipment and rules, while ensuring that the resulting cipher is suitable for telegraph communication.

A message may be re-enciphered two or more times using a different key word each time or it may be enciphered by one method and re-enciphered by another method, using the same or a different key word. Complicated cipher systems requiring the memorizing of, or reference to, numerous rules have been devised for special purposes. Such systems usually fail utterly if there are any errors in transmission and it will be seen later that such errors are very common.

A message can be encrypted two or more times using a different keyword each time, or it can be encrypted by one method and then re-encrypted by another method, using either the same or a different keyword. Complex cipher systems that require memorizing or referencing multiple rules have been created for specific purposes. However, these systems typically fail completely if there are any errors in transmission, and as will be shown later, such errors are quite common.

There are several ingenious cipher machines by which complicated ciphers can be formed, but if the apparatus is available and fairly long messages are at hand for examination, it is usually possible to solve them. Such machines are not, as a rule, simple and small enough for field use; and it must always be remembered that a machine cipher operates on certain mechanical cycles, which can be determined if the machine is available.

There are several clever cipher machines that can create complex ciphers, but if the equipment is available and there are fairly lengthy messages to analyze, it's usually possible to crack them. These machines are generally not simple or small enough for use in the field; and it's important to remember that a machine cipher works on specific mechanical cycles, which can be identified if the machine is accessible.

A book by Commandant Bazeries, entitled “Etude sur la Cryptographie Militaire,” and a series of [91]articles by A. Collon, entitled “Etude sur la Cryptographie,” which appeared in the Revue de L’Armée Belge, 1899–1902, give illustrations and details of operation of several of these cipher machines and the latter goes into the methods of deciphering messages enciphered with them. These methods of analysis require long messages, and as each one is adapted only to the product of a certain machine or apparatus, it is not considered advisable to include a discussion of them here. Those interested in such advanced cipher work must refer to these and other European authors on the subject.

A book by Commandant Bazeries called “Study on Military Cryptography,” along with a series of [__A_TAG_PLACEHOLDER_0__] articles by A. Collon titled “Study on Cryptography,” published in the Belgian Army Review from 1899 to 1902, provide illustrations and details on the operation of several cipher machines. The latter also discusses how to decipher messages encoded with these machines. These analytical methods require lengthy messages, and since each method is only suitable for the output of a specific machine or device, it’s not advisable to cover them here. Those interested in more advanced cipher techniques should refer to these and other European authors on the topic.

The requirement that cipher messages should be adapted to telegraphic transmission, practically excludes ciphers in which three or more letters or whole words are substituted for each letter of the plain text. Such ciphers might be used for the transmission of very short messages but in no other case.

The need for cipher messages to be suitable for telegraphic transmission basically rules out ciphers where three or more letters or entire words are substituted for each letter of the plain text. These ciphers could work for sending very short messages but wouldn’t be viable in other situations.

The cipher of Case 7, with a key word or phrase longer than one-fourth of the message, the cipher after the method of Case 7, using a certain page of a book as a key, and the cipher with a running key, where each letter of the cipher is the key for enciphering the next letter, all look safe and desirable, theoretically, but, practically, the work of enciphering and deciphering is hopelessly slow, and errors in enciphering or transmission make deciphering very difficult. Incidentally the first and second of these ciphers can be solved by the special solution for Case 7, and the third can be solved by trying each of the twenty-six letters of the alphabet as the first key letter, and then continuing the work for five or six letters of the cipher. When the proper primary key letter is found, the solution of the next five or six letters of the cipher will make sense, and thereafter the cipher offers no difficulty. [92]

The cipher in Case 7, which uses a keyword or phrase longer than a quarter of the message, along with the cipher from Case 7 that relies on a specific page of a book as a key, and the cipher with a running key—where each letter of the cipher serves as the key for encoding the next letter—seem secure and appealing in theory. However, in practice, the process of encoding and decoding is incredibly slow, and mistakes in encoding or transmission make decryption quite challenging. Additionally, the first two types of these ciphers can be solved using the special solution for Case 7, while the third can be cracked by testing each of the twenty-six letters of the alphabet as the initial key letter, and then working through the next five or six letters of the cipher. Once the correct primary key letter is found, the solution for the following five or six letters of the cipher becomes clear, and from that point on, the cipher presents no further challenges. [__A_TAG_PLACEHOLDER_0__]

There are numerous other methods of preparing what is virtually a very long, or even an indefinitely long key from a short key word, but all such cipher methods have the same practical disadvantages of slowness of operation and difficulty in deciphering, if errors of enciphering or transmission have been made.

There are many other ways to create what is essentially a very long or even unlimited key from a short keyword, but all these cipher methods come with the same practical downsides: they operate slowly and are tough to decipher if there have been mistakes in encoding or transmission.

The ciphers of Napoleon were long series of numbers representing letters, syllables and words. They were really codes; and a code based on these principles, but using letters instead of numerals, might be evolved very easily. The War Department Code, the Western Union Code, and, in fact, all codes are nothing but specialized substitution ciphers in which each code word represents a letter, word or phrase of the plain text.

The ciphers of Napoleon were long sequences of numbers that stood for letters, syllables, and words. They were essentially codes, and it would be quite easy to create a code based on these ideas but using letters instead of numbers. The War Department Code, the Western Union Code, and really all codes are just specialized substitution ciphers where each code word represents a letter, word, or phrase of the plain text.

Combined Transposition and Substitution Methods

It is evident that a message can be enciphered by any transposition method, and the result enciphered again by any substitution method, or vice versa. But this takes time and leads to errors in the work, so that, if such a process is employed, the substitution and transposition ciphers used are likely to be very simple ones which can be operated with fair rapidity.

It’s clear that a message can be coded using any transposition method, and then encoded again using any substitution method, or the other way around. However, this is time-consuming and can cause mistakes, so if this process is used, the substitution and transposition ciphers employed are likely to be quite simple ones that can be managed fairly quickly.

On preliminary determination, a cipher prepared by such a combination of methods will appear to be a substitution cipher to be solved as such. The frequency table of the result will resemble the normal frequency table, although the message will still be unintelligible and we will know at once that it is a transposition cipher for further solution.

On initial assessment, a code created using this combination of methods will look like a substitution cipher and will be treated as one. The frequency table of the outcome will look similar to a standard frequency table, even though the message will still be unclear, and we will recognize immediately that it is a transposition cipher that needs more work to solve.

The substitution methods usually found in combination ciphers are those of Case 4, 5 and 6, and the transposition method is nearly always Case 1, and particularly the simple varieties of this case like the [93]fence rail (Case 1-i), reversed writing or vertical writing.

The substitution methods typically seen in combination ciphers are those from Case 4, 5, and 6, while the transposition method is almost always Case 1, especially the simpler types of this case like the [__A_TAG_PLACEHOLDER_0__]fence rail (Case 1-i), reversed writing, or vertical writing.

A few examples will show some of the possible combinations.

A few examples will illustrate some of the possible combinations.

The first line of the message of Case 4-a is:

OBQFOBPBRP

We might write it BFBBPOQOPR (Case 1-i), or PRBPBOFQBO (Case 1, reversed writing), or OFQBOPRBPB (Case 1, reversed by groups of five).

We could write it BFBBPOQOPR (Case 1-i), or PRBPBOFQBO (Case 1, reversed writing), or OFQBOPRBPB (Case 1, reversed in groups of five).

The first line of the message of Case 2-b is:

SLCOF WEETN EBRDO ORVYM FFEDI

SLOCF WEETN EBRDO OF MY FFEDI

We might write it TMDPG XFFUO FCSEP PSWZN GGFEJ, or RKBNE VDDSM DAQCN NQUXL EEDCH (Case 4-a, going forward one letter or back one letter).

We could write it TMDPG XFFUO FCSEP PSWZN GGFEJ, or RKBNE VDDSM DAQCN NQUXL EEDCH (Case 4-a, by shifting one letter forward or one letter back).

These examples give an idea of the use of combination methods. It is very rare to find both complicated transposition and substitution methods used in combination. If one is complicated, the other will usually be very simple; and ordinarily both are simple, the sender depending on the combination of the two to attain indecipherability. It is evident how futile this idea is.

These examples illustrate the use of combination methods. It’s very uncommon to see both complex transposition and substitution methods used together. If one method is complex, the other is typically very simple; and usually, both are simple, with the sender relying on the combination of the two to achieve indecipherability. It’s clear how pointless this idea is.

Methods of Enciphering Numerals

It is frequently desirable to send numerals in the body of a cipher message. Several cipher systems prescribe that all numerals in the body of a message must be spelled out; and, while there is no doubt but that this insures greater accuracy, it also greatly increases the length of such messages. In most systems in which it is permissible to send numerals, the following system is used. An indicator, one of the little used letters and especially X, is interpolated before and after the numeral or numerals to be enciphered, and then, for each numeral, a letter is substituted using this or a similar table:

It’s often necessary to include numbers in a cipher message. Many cipher systems require that all numbers in the message must be written out in words; while this does ensure greater accuracy, it also significantly lengthens the messages. In most systems where it’s allowed to send numbers, the following method is used. An indicator, which is one of the less frequently used letters, especially X, is placed before and after the number or numbers to be encoded, and then, for each number, a letter is replaced using this or a similar table:

1	2	3	4	5	6	7	8	9	0
A	B	C	D	E	F	G	H	I	J

[94]

[__A_TAG_PLACEHOLDER_0__]

The enciphering of the message then proceeds, dealing with the indicator and substituted letters as if they were the letters of a word. The decipherer arriving at an X, a series of the letters of the above table and another X, casts out the X’s and substitutes numbers for the letters.

The encoding of the message then continues, treating the indicator and substituted letters like they are the letters of a word. The decipherer reaches an X, a sequence of the letters from the table above and another X, removes the X’s and replaces the letters with numbers.

Sometimes no indicator is used, but the system of substitution of a certain letter for each numeral is followed. Again, the indicator NR may be used instead of a single letter.

Sometimes no indicator is used, but a system is followed where a specific letter substitutes for each numeral. Alternatively, the indicator NR may be used instead of a single letter.

Conventional letters may also be substituted for special characters like ?, $, ”, -, and periods and commas, but this is rarely done except for the period and question mark. The context will usually determine the meaning of such letters when found. In this connection, the use of X to represent end of a sentence and Q to represent a question mark is quite common. [95]

Conventional letters can also replace special characters like ?, $, ”, -, and periods and commas, but this rarely happens except for periods and question marks. The context usually clarifies the meaning of such letters when they're used. In this regard, using X to indicate the end of a sentence and Q for a question mark is quite common. [__A_TAG_PLACEHOLDER_0__]

Chapter X

Errors in Enciphering and Transmission

One of the most difficult tasks before the cipher expert, is the correction of errors which creep into cipher texts in the process of enciphering and transmission by telegraph or radio.

One of the toughest jobs for a cipher expert is fixing the errors that sneak into cipher texts during the process of encoding and sending them via telegraph or radio.

In some cipher methods a mistake in enciphering one letter, or the omission of one letter, will so mix up the deciphering process that only one familiar with such errors can apply the necessary corrections.

In some cipher methods, making a mistake when encoding one letter or leaving out a letter can mess up the decoding process so much that only someone who knows about these kinds of errors can fix it.

The transmission of cipher text over the telegraph or by radio is a slow process, and many fairly good operators cannot receive such matter satisfactorily, because they listen for words and guess at letters at times. The spaced letters in American Morse are the cause of so many errors in code transmission that the War Department Code does not employ any groups using them. In fact, this code is limited to the letters

The sending of cipher text through the telegraph or radio is a slow process, and many decent operators struggle to receive it accurately because they tend to listen for words and sometimes guess at letters. The spaced letters in American Morse lead to numerous errors in code transmission, which is why the War Department Code avoids using any groups that include them. In fact, this code is restricted to the letters

so that there may be a minimum of such confusion.

so that there can be as little confusion as possible.

In cipher work it is necessary, under ordinary circumstances, to use any or all of the letters of the alphabet. To assist operators in keeping the text straight, it is customary to divide cipher text into groups of four, five, six or ten letters, and usually groups of five letters are used. The receiving operator may then expect five letters per group, and if he receives more or less he is sure that either he or the sending operator has made an error. This division into groups of a constant number of letters eliminates word forms and, in the mind of the non-expert, increases [96]the difficulty of solving the cipher. But the increase in difficulty is more apparent than real; particularly, as a cipher examiner habitually finds himself dealing with ciphers without word forms, and the occurrence of a cipher with word forms usually means that he has an easy one to handle.

In cipher work, it's usually necessary to use any or all of the letters in the alphabet. To help operators keep the text organized, it's common to break cipher text into groups of four, five, six, or ten letters, with five-letter groups being the standard. This way, the receiving operator can expect five letters per group, and if they receive more or fewer, they know that either they or the sending operator has made a mistake. Dividing the text into groups of a fixed number of letters removes recognizable word forms and, for someone who isn't an expert, makes the cipher seem harder to crack. However, the increased difficulty is more of an illusion; in reality, a cipher examiner often works with ciphers that don’t have recognizable word forms, and when a cipher does contain word forms, it typically means they have an easier task ahead.

Messages are occasionally encountered which consist partly of plain text and partly of cipher. The cipher part may or may not retain its word forms, but, when this method is used, it is clearly impossible to have a fixed number of letters in each cipher group if the word forms are not used. It is almost impossible to prevent errors of transmission in such messages, and it often requires considerable skill and labor to correct them.

Messages sometimes contain both regular text and coded sections. The coded part might keep its original word shapes or not, but when this approach is taken, it’s obvious that you can’t have a consistent number of letters in each coded group if the word shapes aren’t preserved. It’s very hard to avoid mistakes in these messages, and correcting them often takes a lot of skill and effort.

For those unfamiliar with the telegraph alphabets, they are given below. Messages sent by commercial or military telegraphs or buzzer lines will be transmitted with the American Morse alphabet. Those sent by radio, visual signalling or submarine cable will be transmitted by Continental Morse, known also as the International Code. Messages may be transmitted by both alphabets in course of transmission. For example, a cablegram from the Philippines to Nome, Alaska, will be transmitted by Continental Morse (commercial cable) from Manila to San Francisco, by American Morse (commercial land line) from San Francisco to Seattle, by Continental Morse (military cable) from Seattle to Valdez, by American Morse (military land line) from Valdez to Nulato and by Continental Morse (military radio) from Nulato to Nome.

For those who aren't familiar with telegraph alphabets, they're listed below. Messages sent through commercial or military telegraphs or buzzer lines will use the American Morse alphabet. Those sent via radio, visual signaling, or submarine cable will be sent using Continental Morse, also known as the International Code. Messages can be transmitted using both alphabets during the process. For instance, a cablegram from the Philippines to Nome, Alaska, will be sent using Continental Morse (commercial cable) from Manila to San Francisco, American Morse (commercial land line) from San Francisco to Seattle, Continental Morse (military cable) from Seattle to Valdez, American Morse (military land line) from Valdez to Nulato, and Continental Morse (military radio) from Nulato to Nome.

Prior to February, 1914, the Mexican government telegraph lines used an alphabet differing slightly from the American and Continental Morse. However, at that time, the Continental Morse alphabet was prescribed for use on these lines and [97]it is believed that the use of the old alphabet has entirely ceased on Mexican lines. However, skilled American operators would have no difficulty in picking up this alphabet if it were found to be in use.

Before February 1914, the telegraph lines in the Mexican government used an alphabet that was slightly different from American and Continental Morse. However, at that time, the Continental Morse alphabet was mandated for use on these lines and [__A_TAG_PLACEHOLDER_0__]it's believed that the old alphabet has completely stopped being used on Mexican lines. Nevertheless, experienced American operators would easily be able to recognize this alphabet if it were still in use.

Radio communication is, by International Convention, invariably in Continental Morse.

Radio communication is, by international agreement, always in Continental Morse.

Telegraph Alphabets

Character	American Morse	Continental Morse or International Code
A	. -	. -
B	- . . .	- . . .
C	. . .	- . - .
D	- . .	- . .
E	.	.
F	. - .	. . - .
G	- - .	- - .
H	. . . .	. . . .
I	. .	. .
J	- . - .	. - - -
K	- . -	- . -
L	—	. - . .
M	- -	- -
N	- .	- .
O	. .	- - -
P	. . . . .	. - - .
Q	. . - .	- - . -
R	. . .	. - .
S	. . .	. . .
T	-	-
U	. . -	. . -
V	. . . -	. . . -
W	. - -	. - -
X	. - . .	- . . -
Y	. . . .	- . - -
Z	. . . .	- - . .
1	. - - .	. - - - -
2	. . - . .	. . - - -
3	. . . - .	. . . - -
4	. . . . -	. . . . -
5	- - -	. . . . .
6	. . . . . .	- . . . .[__A_TAG_PLACEHOLDER_0__]
7	- - . .	- - . . .
8	- . . . .	- - - . .
9	- . . -	- - - - .
0	——	- - - - -
Period	. . - - . .	Sure! Please provide the text you would like me to modernize.
Question Mark	- . . - .	. . - - . .
Comma	. - . -	- - . . - -

The following example will show some of the errors that creep into messages prepared with the cipher disk and transmitted by radio:

The following example will show some of the mistakes that slip into messages created with the cipher disk and sent by radio:

Message

Message

Radio Douglas de El Paso, 2 H 71, twenty-fifth, 9:00 a.m., Govt. To C.O., Sixth Brigade, Douglas, Arizona:

JPRZI RDJSG XTRMJ USFPC RECLA BCPCB OAXPK QEQKF PPZAE BKUTT JHWEU AHPZE EZOLT HKXPH KIHAV DRODN IAPZC LVUMP KFUBV VTVNV EFVZV TLVQS BKAHQ NVKVF MGJTH OWBGN WWEPO LJKFP HEXKW CPDLZ JWSQC JVKIG HTJHT EGAHA GDXXK BSPPK DIAVZ VQONC HOVDA VZQKW FNVON RPVGH CUFPV SFPIE TOZOD WGYFE AWNJY KOEDW UMELD NOBUH MUPQL GYOPP ODBAB UFUUC AEOJW RDIPK WMOKV OMICW CKPIH LUMSY YOSBG WOPHV PKOMO PHGER

Smith.

The key word is ATCHISON, the cipher disk being used and the setting changed for every letter of the message. The letter X indicates a period where it is evidently not a letter of a word.

The key word is ATCHISON, with the cipher disk being used and the settings changing for each letter of the message. The letter X marks a period where it clearly isn't part of a word.

Deciphering the message with this key and method we have:

Decoding the message with this key and method we have:

RELIA BLEIN FORGF TIONF ROMCA SASGR ANDES RECEI LEDHE RETHA TAMOU NTEDD ETACH MSKTL EFTTH ERELA STNIG HTTOE SCORT SHYMP ENTOF ARMSA NDAMM UNITI ONTOB ESMUG GLEDA CRJXS BORDE RNEXT FRIDA YNIGH TATAP OINTT WELVE MIENX FKOSB

RELIABLE INFORMATION FROM CASAGRANDES RECEIVED HERE STATES THAT EACH MASK LEFT THERE LAST NIGHT IS TO ESCORT A SHIPMENT OF ARMS AND AMMUNITION TO BE SMUGGLED ACROSS THE BORDER NEXT FRIDAY NIGHT AT A POINT TWELVE MINUTES.

Beyond this point the message, if we continue the deciphering process, is unintelligible. The sense fails at the first P of the cipher group BSPPK. We have translated B as M with disk A to N and S as I with disk A to A. The last words that make sense [99]are A POINT TWELVE MI; clearly the rest of the last word is LES and this is represented by PPK. Putting P=L then A=A and putting P=E then A=T. In other words, the encipherer forgot to change his disk setting, A to A, after enciphering I into S and enciphered L into P with the same setting, A to A. Continuing the deciphering on this basis, we have:

Beyond this point, the message becomes unintelligible if we keep trying to decode it. The meaning breaks down at the first P of the cipher group BSPPK. We translated B as M with disk A to N, and S as I with disk A to A. The last words that make sense [__A_TAG_PLACEHOLDER_0__] are A POINT 12 MI; it’s clear the rest of the last word is LES, represented by PPK. If we set P=L, then A=A, and if we set P=E, then A=T. In other words, the person encoding it forgot to change their disk setting from A to A after encoding I into S, and encoded L into P using the same setting, A to A. Continuing the decoding based on this, we have:

LES EASTO FDOUG LAS.T HISIS INYOU RDIST RICT. WILLY OUTAK ENECE SSARV STEPS TOPRE VENTT HISSH IPMEN TFROM GOING SKZRX LEADE ROFSM UGGLE RSSAL DTOBE JUANH ERNAN DEZOF NACO.

LES EASTO FDOUG LAS.T THIS IS IN YOUR DISTRICT. WILL YOU TAKE NECESSARYV STEPS TO PREVENT THIS SHIPMENT FROM GOING SKZRX? LEADERS OF MUGGLERS SALD TO BE JUAN HERNAN DEZ OF NACO.

The minor errors underlined above are not difficult to correct except the sixth word in the eighth line. They will be taken up however for analysis of cause of error.

The minor errors highlighted above are easy to fix except for the sixth word in the eighth line. They will be addressed for an analysis of the cause of the error.

Line 1, GF should be MA. Putting the latter into cipher we find the letters of the cipher should have been GO instead of MJ. This is clearly a telegrapher’s error, --. --- becoming -- .---

Line 1, GF should be MA. When we encode the latter, we discover that the letters in the cipher should have been Understood. Please provide the text you would like me to modernize. instead of MJ. This is clearly a telegrapher’s mistake, --. --- becoming -- .---

Line 2, L should be V. The corresponding cipher letter should be F instead of P. This is an error of the encipherer in copying.

Line 2, L should be V. The corresponding cipher letter should be F instead of P. This is a copying error by the encipherer.

Line 2, SK should be EN. The corresponding cipher letters should be YU instead of KX. Another telegrapher’s error, -.-- ..- becoming -.- -..-

Line 3, Y should be I. The corresponding cipher letter should be L instead of V. Another error in copying by the encipherer.

Line 3, Y should be I. The corresponding cipher letter should be L instead of V. Another mistake made by the encipherer.

Line 4, JX should be OS. The corresponding cipher letters should be FK instead of KF; an error on the part of the encipherer in copying.

Line 4, JX should be OS. The corresponding cipher letters should be FK instead of KF; a mistake made by the encipherer while copying.

Line 7, V should be Y. A mistake in copying.

Line 8, SKZRX. If we take X as a period, then this line might be OVER, the R being correct and [100]SKZ being in question. The corresponding cipher letters are AEO and if we encipher OVE we get ETJ. Here again we have a telegrapher’s error, . - .--- becoming .- . ---

Line 8, SKZRX. If we consider X as a period, then this line might be OVER, with the R being correct and [__A_TAG_PLACEHOLDER_0__]SKZ being in question. The corresponding cipher letters are AEO, and if we encipher OVE we get ETJ. Here again we have a telegrapher’s error, . - .--- becoming .- .---

Line 9, L should be I. The corresponding cipher letter should be K instead of H; an error in copying by the encipherer.

Line 9, L should be I. The corresponding cipher letter should be K instead of H; a mistake made by the person doing the encoding.

The errors by the encipherer above noted are fairly common ones. These and similar errors are usually found when a cipher message, prepared as a rough draft by the encipherer, is copied by a clerk and a careful check of the copy is not made. The letters mistaken depend, of course, on the encipherer’s hand writing or printing. Other errors, besides those noted, are the confusion of C, G, and Q; I, and J; B and R, etc.

The mistakes made by the encipherer mentioned above are quite common. These and similar mistakes usually occur when a cipher message, drafted roughly by the encipherer, is copied by a clerk without a careful review of the copy. The letters that get confused depend, of course, on the encipherer’s handwriting or printing. Other errors, in addition to those mentioned, include confusion between C, G, and Q; I and J; B and R, etc.

The error by the encipherer, in not changing his disk setting for one letter and thus throwing out the whole process of deciphering, would not have occurred had he put the message into eight columns or a multiple thereof and enciphered each column with one disk setting. This latter method is also very much faster.

The mistake made by the person encoding the message, by not changing the disk setting for one letter and ruining the entire decoding process, wouldn’t have happened if he had arranged the message into eight columns or a multiple of that and encoded each column using one disk setting. This method is also much quicker.

Telegraphers’ errors in cipher transmission are common and often very confusing. Note should be taken as to whether Continental or American Morse was used for transmission. An analysis along the lines indicated will usually develop the error and correction. If not, a repetition should be demanded, calling attention, if possible, to the particular groups that are not clear.

Telegraphers’ mistakes in sending coded messages are common and can be really confusing. It’s important to note whether Continental or American Morse was used for the transmission. An analysis based on these points will typically reveal the error and the correction. If that doesn’t work, a repeat should be requested, highlighting the specific groups that aren’t clear, if possible.

The deciphered and corrected message is:

The decoded and revised message is:

“Reliable information from Casas Grandes received here that a mounted detachment left there last night to escort shipment of arms and ammunition to be smuggled across border next Friday night, at a point twelve miles east of Douglas. This is in [101]your district. Will you take necessary steps to prevent this shipment going over? Leader of smugglers said to be Juan Hernandez of Naco.”

“Reliable information from Casas Grandes here indicates that a mounted detachment left last night to escort a shipment of arms and ammunition that will be smuggled across the border next Friday night, at a location twelve miles east of Douglas. This is in [__A_TAG_PLACEHOLDER_0__]your district. Will you take the necessary steps to stop this shipment? The leader of the smugglers is said to be Juan Hernandez of Naco.”

Another remarkable example of errors in transmission by American Morse is the following: A message, partly in cipher and partly in plain text, contained the cipher words

Another notable example of transmission errors by American Morse is this: A message, which was partly in code and partly in plain text, included the coded words

GA GTXIEIT EIDISXQ

This, deciphered as far as possible by the alphabet determined by analysis of the rest of the cipher, read

This, interpreted as much as possible by the alphabet figured out through analyzing the rest of the cipher, read

SU SME_Y_M Y_O_GES

MY SUGGESTIONS

It was finally decided that the context required a single word like SUSPENDIO or SUSPENDIOLES for this cipher group. An examination along this line showed that the cipher words should have been

It was finally decided that the context needed a single word like SUSPENDIO or SUSPENDIOLES for this cipher group. An examination along this line showed that the cipher words should have been

received

and were received

and that there were five errors in transmission in these three cipher groups alone.

and that there were five errors in transmission in just these three cipher groups.

Colophon

Availability

Scans for this book are available from the Internet Archive (copy 1).

Library of Congress Classification: UB290 .H5.

Related Library of Congress catalog page: war16000058.

Related Open Library catalog page (for source): OL7044123M.

Related Open Library catalog page (for work): OL92027W.

Encoding

Library of Congress Subject HeadingsLibrary of Congress Classification

Revision History

2011-12-15 Started.

External References

Corrections

The following corrections have been applied to the text:

The following corrections have been made to the text:

Page	Source	Correction
1	messages	message
17	[Not in source]	,
22	begining	beginning
27	b	d
28	of	or
37	Kirckhoff’s	Kerckhoffs’
44	preceeding	preceding
49	WE	We
51	identfied	identified
63	[Not in source]	.
66	[Not in source]	)
67	0	2
67	[Not in source]	1
89	.	:
98	. . . . . .	. - . - . -
98	. - . - . -	- - . . - -

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	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
A		1	7	10	22	3	2	26	4	2	2	7	8	11	2	9		13	12	9		2	4	1	12
B	5			1	2				1			1	1	1	2				2	1	3				1
C	6		1	1	14	2			11					11	3			2	3	1	1		1		1
D	6			12	30	1			2			4		30	1			4	1	1	1		1		3
E		11	14	16	12	2	6	33	10	2	6	18	14	12	1	7		36	11	12	2	16	5		1	1
F	3			2	8	2	1		2			2	1	3	25				3	1	1				1
G	4			1	3				2					11	2			3							1
H	1		11	2	4	1	4					1		2	1	1		2	10	50			3		2
I	2	1	4	12	6	5	1	12	1		5	9	8	12	1	3		12	13	22	2	3	6		1	1
J		1
K	1		1		2													2	1		1
L	14	6	2	1	6	1	1	1	6			9		3	6	3		3	2	3	5
M	7			3	13	2		2	3				4	1	10			4	1	1					2
N	38			3	25		2	1	31		3		2	2	39			4	3		11		2
O	1	1	12	4	8	8	3	12	18	2		4	7	8	3	7		13	15	22		2	6	1	5
P	2			1	8				1			2	4	2	3	2		1	8	1	4			3	1
Q					2									1	1				1
R	16	1	3	3	40	3	6	2	6			1	2	1	25	8		2	2	8	11				2
S	16	1		3	25	1	2		17		1	2	1	12	7	2		9	11	6	11		1		6
T	25	1	3	12	13	5	2	3	20			2	1	24	8	2		16	20	11	6		2	2	7
U	1	2	1	6	1	3	2	2		3		3	1		17	1	5	3	5	5				1
V	3	1			5				5						3			2			5				1
W	1			2	8		1	1				1	1	2	4				2	3					3
X	1				4				2						1						1
Y	3	2		2	4		1	1				8	1	2		1		3	1	7
Z	1								1					1
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z

TH	50	AT	25	ST	20
ER	40	EN	25	IO	18
ON	39	ES	25	LE	18
AN	38	OF	25	IS	17
RE	36	OR	25	OU	17
HE	33	NT	24	AR	16
IN	31	EA	22	AS	16
ED	30	TI	22	DE	16
ND	30	TO	22	RT	16
HA	26	IT	20	VE	16

THE	89	TIO	33	EDT	27
AND	54	FOR	33	TIS	25
THA	47	NDE	31	OFT	23
ENT	39	HAS	28	STH	21
ION	36	NCE	27	MEN	20

	A	B	C	D	E	F	G	H	I	J	L	M	N	O	P	Q	R	S	T	U	V	X	Y	Z
A	9	4	19	11	5		6	17	23		54	18	9	3	20		29	11	21	8	6		2	5	A
B	6								3			1		4											B
C	24		6	6	24				5		3		8	8			9	5		2			2		C
D	31				29				3				19	13			10	9					4		D
E	12	2	6	59	10		1	5	7	2	12	18	22	4	9		38	25	28	25	3		3		E
F	4				4						4		3					3					1		F
G	2				4				8				4											2	G
H	2		12		10													2					1		H
I	2		23	16		5	2				3	11	13				6	10	5		3				I
J	3				2								1												J
L	21	3	6		39	3	3		7		21		5	6			12	2		2					L
M	12				6				5		1		6	15			7	2		6			1		M
N	32				46		2		8					32						12			2		N
O			26	22	2	6	3	4	9		16	2	8		20		15	7	11						O
P	13				3				2		4	9	2	7			4	11							P
Q	11	5									1		2				3		1						Q
R	40				27	2			4		4			36	3		11		17	3					R
S	39				52				10				7	14			2			14			3		S
T	5				13				4		4		18	5			6	30							T
U	2		4	2	6	3	4			5		2	6		4	17		15	2				1		U
V	2				2						2			2				2					2		V
X																									X
Y	5				6									2				5		2				2	Y
Z	1				2								1				4			2					Z
	A	B	C	D	E	F	G	H	I	J	L	M	N	O	P	Q	R	S	T	U	V	X	Y	Z

DE	59	ON	32	AC	24
LA	54	AD	31	EC	24
ES	52	ST	30	CI	23
EN	46	ED	29	IA	23
AR	40	RA	29	DO	22
AS	39	TE	28	NE	22
EL	39	ER	27	AL	21
RE	38	CO	26	LL	21
OR	36	SE	25	PA	20
AN	32	UE	25	PO	20

1	2	3	4	5	6	7	8	9	10	11	12
H	I	I	G	F	T	N	G	H	I	N	T
C	V	N	I	E	I	O	T	C	Y	I	F
Y	L	H	A	E	A	E	S	N	B	A	E
E	E	E	N	R	W	G	B	N	Y	D	E
L	R	O	A	E	S	G	R	N	E	B	O
V	N	L	D	A	I	C	A	O	A	L	C
N	D	T	I	R	G	V	A	C	D	O	I
E	S	E	R	E	C	D	V	P	E	I	A
F	I	F	L	R	I	N	E	H	E	T	T

1	6	2	4	5	2
H	T	I	G	F	I
C	I	V	I	E	V
Y	A	L	A	E	L
E	W	E	N	R	E
L	S	R	A	E	R
V	I	N	D	A	N
N	G	D	I	R	D
E	C	S	R	E	S
F	I	I	L	R	I

5	2	4	1	6	3
F	I	G	H	T	I
E	V	I	C	I	N
E	L	A	Y	A	H
R	E	N	E	W	E
E	R	A	L	S	O
A	N	D	V	I	L
R	D	I	N	G	T
E	S	R	E	C	E
R	I	L	F	I	F

	1	2	3	4	5	6	7	8	9	10
1	W	V	G	A	E	E	G	E	N	L
2	T	F	T	O	H	T	E	I	E	F
3	R	B	T	S	E	I	N	E	N	G
4	O	N	W	R	M	G	X	I	X	N
5	G	O	I	T	N	R	O	M	R	O
6	E	S	P	A	L	H	N	E	A	C
7	U	D	N	N	H	D	E	R	M	E

	3	5	1	4	2	8	10	6	9	7
1	G	E	W	A	V	E	L	E	N	G
2	T	H	T	O	F	I	F	T	E	E
3	T	E	R	S	B	E	G	I	N	N
4	W	M	O	R	N	I	N	G	X	X
5	I	N	G	T	O	M	O	R	R	O
6	P	L	E	A	S	E	C	H	A	N
7	N	H	U	N	D	R	E	D	M	E

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
A		1	7	10	22	3	2	26	4	2	2	7	8	11	2	9		13	12	9		2	4	1	12
B	5			1	2				1			1	1	1	2				2	1	3				1
C	6		1	1	14	2			11					11	3			2	3	1	1		1		1
D	6			12	30	1			2			4		30	1			4	1	1	1		1		3
E		11	14	16	12	2	6	33	10	2	6	18	14	12	1	7		36	11	12	2	16	5		1	1
F	3			2	8	2	1		2			2	1	3	25				3	1	1				1
G	4			1	3				2					11	2			3							1
H	1		11	2	4	1	4					1		2	1	1		2	10	50			3		2
I	2	1	4	12	6	5	1	12	1		5	9	8	12	1	3		12	13	22	2	3	6		1	1
J		1
K	1		1		2													2	1		1
L	14	6	2	1	6	1	1	1	6			9		3	6	3		3	2	3	5
M	7			3	13	2		2	3				4	1	10			4	1	1					2
N	38			3	25		2	1	31		3		2	2	39			4	3		11		2
O	1	1	12	4	8	8	3	12	18	2		4	7	8	3	7		13	15	22		2	6	1	5
P	2			1	8				1			2	4	2	3	2		1	8	1	4			3	1
Q					2									1	1				1
R	16	1	3	3	40	3	6	2	6			1	2	1	25	8		2	2	8	11				2
S	16	1		3	25	1	2		17		1	2	1	12	7	2		9	11	6	11		1		6
T	25	1	3	12	13	5	2	3	20			2	1	24	8	2		16	20	11	6		2	2	7
U	1	2	1	6	1	3	2	2		3		3	1		17	1	5	3	5	5				1
V	3	1			5				5						3			2			5				1
W	1			2	8		1	1				1	1	2	4				2	3					3
X	1				4				2						1						1
Y	3	2		2	4		1	1				8	1	2		1		3	1	7
Z	1								1					1
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z

TH	50	AT	25	ST	20
ER	40	EN	25	IO	18
ON	39	ES	25	LE	18
AN	38	OF	25	IS	17
RE	36	OR	25	OU	17
HE	33	NT	24	AR	16
IN	31	EA	22	AS	16
ED	30	TI	22	DE	16
ND	30	TO	22	RT	16
HA	26	IT	20	VE	16

THE	89	TIO	33	EDT	27
AND	54	FOR	33	TIS	25
THA	47	NDE	31	OFT	23
ENT	39	HAS	28	STH	21
ION	36	NCE	27	MEN	20

	A	B	C	D	E	F	G	H	I	J	L	M	N	O	P	Q	R	S	T	U	V	X	Y	Z
A	9	4	19	11	5		6	17	23		54	18	9	3	20		29	11	21	8	6		2	5	A
B	6								3			1		4											B
C	24		6	6	24				5		3		8	8			9	5		2			2		C
D	31				29				3				19	13			10	9					4		D
E	12	2	6	59	10		1	5	7	2	12	18	22	4	9		38	25	28	25	3		3		E
F	4				4						4		3					3					1		F
G	2				4				8				4											2	G
H	2		12		10													2					1		H
I	2		23	16		5	2				3	11	13				6	10	5		3				I
J	3				2								1												J
L	21	3	6		39	3	3		7		21		5	6			12	2		2					L
M	12				6				5		1		6	15			7	2		6			1		M
N	32				46		2		8					32						12			2		N
O			26	22	2	6	3	4	9		16	2	8		20		15	7	11						O
P	13				3				2		4	9	2	7			4	11							P
Q	11	5									1		2				3		1						Q
R	40				27	2			4		4			36	3		11		17	3					R
S	39				52				10				7	14			2			14			3		S
T	5				13				4		4		18	5			6	30							T
U	2		4	2	6	3	4			5		2	6		4	17		15	2				1		U
V	2				2						2			2				2					2		V
X																									X
Y	5				6									2				5		2				2	Y
Z	1				2								1				4			2					Z
	A	B	C	D	E	F	G	H	I	J	L	M	N	O	P	Q	R	S	T	U	V	X	Y	Z

DE	59	ON	32	AC	24
LA	54	AD	31	EC	24
ES	52	ST	30	CI	23
EN	46	ED	29	IA	23
AR	40	RA	29	DO	22
AS	39	TE	28	NE	22
EL	39	ER	27	AL	21
RE	38	CO	26	LL	21
OR	36	SE	25	PA	20
AN	32	UE	25	PO	20

1	2	3	4	5	6	7	8	9	10	11	12
H	I	I	G	F	T	N	G	H	I	N	T
C	V	N	I	E	I	O	T	C	Y	I	F
Y	L	H	A	E	A	E	S	N	B	A	E
E	E	E	N	R	W	G	B	N	Y	D	E
L	R	O	A	E	S	G	R	N	E	B	O
V	N	L	D	A	I	C	A	O	A	L	C
N	D	T	I	R	G	V	A	C	D	O	I
E	S	E	R	E	C	D	V	P	E	I	A
F	I	F	L	R	I	N	E	H	E	T	T

1	6	2	4	5	2
H	T	I	G	F	I
C	I	V	I	E	V
Y	A	L	A	E	L
E	W	E	N	R	E
L	S	R	A	E	R
V	I	N	D	A	N
N	G	D	I	R	D
E	C	S	R	E	S
F	I	I	L	R	I

5	2	4	1	6	3
F	I	G	H	T	I
E	V	I	C	I	N
E	L	A	Y	A	H
R	E	N	E	W	E
E	R	A	L	S	O
A	N	D	V	I	L
R	D	I	N	G	T
E	S	R	E	C	E
R	I	L	F	I	F

	1	2	3	4	5	6	7	8	9	10
1	W	V	G	A	E	E	G	E	N	L
2	T	F	T	O	H	T	E	I	E	F
3	R	B	T	S	E	I	N	E	N	G
4	O	N	W	R	M	G	X	I	X	N
5	G	O	I	T	N	R	O	M	R	O
6	E	S	P	A	L	H	N	E	A	C
7	U	D	N	N	H	D	E	R	M	E

	3	5	1	4	2	8	10	6	9	7
1	G	E	W	A	V	E	L	E	N	G
2	T	H	T	O	F	I	F	T	E	E
3	T	E	R	S	B	E	G	I	N	N
4	W	M	O	R	N	I	N	G	X	X
5	I	N	G	T	O	M	O	R	R	O
6	P	L	E	A	S	E	C	H	A	N
7	N	H	U	N	D	R	E	D	M	E

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z
A		1	7	10	22	3	2	26	4	2	2	7	8	11	2	9		13	12	9		2	4	1	12
B	5			1	2				1			1	1	1	2				2	1	3				1
C	6		1	1	14	2			11					11	3			2	3	1	1		1		1
D	6			12	30	1			2			4		30	1			4	1	1	1		1		3
E		11	14	16	12	2	6	33	10	2	6	18	14	12	1	7		36	11	12	2	16	5		1	1
F	3			2	8	2	1		2			2	1	3	25				3	1	1				1
G	4			1	3				2					11	2			3							1
H	1		11	2	4	1	4					1		2	1	1		2	10	50			3		2
I	2	1	4	12	6	5	1	12	1		5	9	8	12	1	3		12	13	22	2	3	6		1	1
J		1
K	1		1		2													2	1		1
L	14	6	2	1	6	1	1	1	6			9		3	6	3		3	2	3	5
M	7			3	13	2		2	3				4	1	10			4	1	1					2
N	38			3	25		2	1	31		3		2	2	39			4	3		11		2
O	1	1	12	4	8	8	3	12	18	2		4	7	8	3	7		13	15	22		2	6	1	5
P	2			1	8				1			2	4	2	3	2		1	8	1	4			3	1
Q					2									1	1				1
R	16	1	3	3	40	3	6	2	6			1	2	1	25	8		2	2	8	11				2
S	16	1		3	25	1	2		17		1	2	1	12	7	2		9	11	6	11		1		6
T	25	1	3	12	13	5	2	3	20			2	1	24	8	2		16	20	11	6		2	2	7
U	1	2	1	6	1	3	2	2		3		3	1		17	1	5	3	5	5				1
V	3	1			5				5						3			2			5				1
W	1			2	8		1	1				1	1	2	4				2	3					3
X	1				4				2						1						1
Y	3	2		2	4		1	1				8	1	2		1		3	1	7
Z	1								1					1
	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	Q	R	S	T	U	V	W	X	Y	Z

TH	50	AT	25	ST	20
ER	40	EN	25	IO	18
ON	39	ES	25	LE	18
AN	38	OF	25	IS	17
RE	36	OR	25	OU	17
HE	33	NT	24	AR	16
IN	31	EA	22	AS	16
ED	30	TI	22	DE	16
ND	30	TO	22	RT	16
HA	26	IT	20	VE	16

THE	89	TIO	33	EDT	27
AND	54	FOR	33	TIS	25
THA	47	NDE	31	OFT	23
ENT	39	HAS	28	STH	21
ION	36	NCE	27	MEN	20

	A	B	C	D	E	F	G	H	I	J	L	M	N	O	P	Q	R	S	T	U	V	X	Y	Z
A	9	4	19	11	5		6	17	23		54	18	9	3	20		29	11	21	8	6		2	5	A
B	6								3			1		4											B
C	24		6	6	24				5		3		8	8			9	5		2			2		C
D	31				29				3				19	13			10	9					4		D
E	12	2	6	59	10		1	5	7	2	12	18	22	4	9		38	25	28	25	3		3		E
F	4				4						4		3					3					1		F
G	2				4				8				4											2	G
H	2		12		10													2					1		H
I	2		23	16		5	2				3	11	13				6	10	5		3				I
J	3				2								1												J
L	21	3	6		39	3	3		7		21		5	6			12	2		2					L
M	12				6				5		1		6	15			7	2		6			1		M
N	32				46		2		8					32						12			2		N
O			26	22	2	6	3	4	9		16	2	8		20		15	7	11						O
P	13				3				2		4	9	2	7			4	11							P
Q	11	5									1		2				3		1						Q
R	40				27	2			4		4			36	3		11		17	3					R
S	39				52				10				7	14			2			14			3		S
T	5				13				4		4		18	5			6	30							T
U	2		4	2	6	3	4			5		2	6		4	17		15	2				1		U
V	2				2						2			2				2					2		V
X																									X
Y	5				6									2				5		2				2	Y
Z	1				2								1				4			2					Z
	A	B	C	D	E	F	G	H	I	J	L	M	N	O	P	Q	R	S	T	U	V	X	Y	Z

DE	59	ON	32	AC	24
LA	54	AD	31	EC	24
ES	52	ST	30	CI	23
EN	46	ED	29	IA	23
AR	40	RA	29	DO	22
AS	39	TE	28	NE	22
EL	39	ER	27	AL	21
RE	38	CO	26	LL	21
OR	36	SE	25	PA	20
AN	32	UE	25	PO	20

1	2	3	4	5	6	7	8	9	10	11	12
H	I	I	G	F	T	N	G	H	I	N	T
C	V	N	I	E	I	O	T	C	Y	I	F
Y	L	H	A	E	A	E	S	N	B	A	E
E	E	E	N	R	W	G	B	N	Y	D	E
L	R	O	A	E	S	G	R	N	E	B	O
V	N	L	D	A	I	C	A	O	A	L	C
N	D	T	I	R	G	V	A	C	D	O	I
E	S	E	R	E	C	D	V	P	E	I	A
F	I	F	L	R	I	N	E	H	E	T	T

1	6	2	4	5	2
H	T	I	G	F	I
C	I	V	I	E	V
Y	A	L	A	E	L
E	W	E	N	R	E
L	S	R	A	E	R
V	I	N	D	A	N
N	G	D	I	R	D
E	C	S	R	E	S
F	I	I	L	R	I

5	2	4	1	6	3
F	I	G	H	T	I
E	V	I	C	I	N
E	L	A	Y	A	H
R	E	N	E	W	E
E	R	A	L	S	O
A	N	D	V	I	L
R	D	I	N	G	T
E	S	R	E	C	E
R	I	L	F	I	F

	1	2	3	4	5	6	7	8	9	10
1	W	V	G	A	E	E	G	E	N	L
2	T	F	T	O	H	T	E	I	E	F
3	R	B	T	S	E	I	N	E	N	G
4	O	N	W	R	M	G	X	I	X	N
5	G	O	I	T	N	R	O	M	R	O
6	E	S	P	A	L	H	N	E	A	C
7	U	D	N	N	H	D	E	R	M	E

	3	5	1	4	2	8	10	6	9	7
1	G	E	W	A	V	E	L	E	N	G
2	T	H	T	O	F	I	F	T	E	E
3	T	E	R	S	B	E	G	I	N	N
4	W	M	O	R	N	I	N	G	X	X
5	I	N	G	T	O	M	O	R	R	O
6	P	L	E	A	S	E	C	H	A	N
7	N	H	U	N	D	R	E	D	M	E