Manual for the Solution of Military Ciphers, Parker Hitt

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. [vi]

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 [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.

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. [1]

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. [2]

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 [3]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. [4]

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 [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.

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.

---

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, [17]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 [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 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 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 [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.

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 [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 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. [22]

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]

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. [24]

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 [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.

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]

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.

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. [40]

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.

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 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.

Using the alphabet indicated by G, we get

Continuing for the other alphabets, we get

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.

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]

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

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.

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.

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.

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:

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

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]

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

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.

A combination of the Vigenere and Porta ciphers is this:

[57]

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.

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

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.

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.

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

“—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:

“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:

“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);

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.

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.