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

MANUAL FOR THE SOLUTION
OF MILITARY CIPHERS

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.

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.

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.

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 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.

Kerckhoffs has stated that a military cipher should fulfill 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.

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 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.

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.

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 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.

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.

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.

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.

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.

As to luck, there is the old miner’s proverb: “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.

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.

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 provided, so that the station can be “listening in” during the entire twenty-four hours.

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 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.

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.

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.

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.

Again there is a fixed ratio of occurrence of 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.

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.

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.

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.

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%.

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.

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

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

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.

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:

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.

Data for the Solution of Ciphers in Spanish

The Spanish language is written with 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 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:

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.

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.

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 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.

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.

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

Order of letters:

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.

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.

Alphabetic Frequency Tables

(Truesdell)

Frequency of occurrence in 1,000 letters of text:

Order of Frequency

French

German

Italian

Portuguese

Graphic Frequency Tables

Frequency of occurrence in 200 letters of text.

French

Italian

German

Portuguese

[1] Occurrence rare, usually 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.

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.

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, such a table will give the best 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.

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 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 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 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.

Intelligence Section, General Staff
1st FieldArmy
----------- ----------- Place, Date
Record ofCipher Examination
This cipher obtainedby ----------- ----------- at ----------- ----------- on ----------- ----------- (date) (hour) How being transmitted when obtained. (Underscore meansused and enter data on sending and receiving stations). Sending Station Receiving Station Radio Telephone Telegraph Buzzer Helio Lantern Flag Cyclist from to Foot Messenger from ,, to ,, Mtd. Messenger from ,, to ,, How obtained. (Underscore means used). Captured beforedelivery to addressee. Captured after delivery to addressee.Intercepted, not received by addressee. Copied, but received byaddressee. Remarks:		Office No. ----------- Received ----------- ----------- (Date) (Hour) From ----------- At ----------- To ----------- At ----------- Date ----------- Probable language of text ----------- Class Transposition ----------- ----------- Substitution ----------- ----------- Case ----------- Remarks: Solution completed --------- ---------- (date) (hour) Language of text ----------- Key, (if determined) ----------- ----------- Type ----------- FileNo. ----------- ----------- ----------- Examiner.

The probable language of the text is assumed from the preceding data and, if necessary, from internal evidence. Thus a cipher from a Mexican source and not containing 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 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.

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 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.

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 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 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 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.

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.

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.

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.

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.

Chapter IV

Classes of Ciphers

There are, in general, two classes 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.

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).

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.

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

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 be 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.

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 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.

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.

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.

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.

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:

(a) Simple Horizontal:

(b) Simple Vertical:

(c) Alternate Horizontal:

(d) Alternate Vertical:

(e) Simple Diagonal:

(f) Alternate Diagonal:

(g) Spiral, clockwise:

(h) Spiral, counter clockwise:

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.

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:

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

Message

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.

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:

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”.

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 following ciphers come 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:

HOSTILE CAVALRY HAS RETIRED

is written:

and is sent:

OTLCV LYART RDHSI EAARH SEIEX

Case 1-j.

Message

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.

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.

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

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.

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

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-a.

Message

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:

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.

These combinations appear among others:

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

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

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.

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 twelve columns. The order 1, 6, 3, 11, 8 was tried and gave this result.

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.

Case 2-b.

Message

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

Among other combinations are:

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.

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.

Message

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

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.

Among other combinations we have these:

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

Although of no particular importance, it may be stated that the column key in this case was GRAND and the line key was CENTRAL, both used as in 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.

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

Here the route 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:

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 the message and the receiver eliminates them before arranging his message in columns to get the sense of 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.

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.

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.

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.

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 by complicated rules, will, on analysis, be seen to be very simple.

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.

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.

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.

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.

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:

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.

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.

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.

Case 4-a.

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:

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.

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.

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.

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.

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 the cipher it is evidence that the regular English alphabet is used.

Case 5-a.

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].

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.

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].

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 form is here presented in order to compare with it the frequency table for the message discussed in [case 4-a].

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 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.

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.

Case 6-a.

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.

Frequency Table