Cryptanalysis

“ The word cryptography, properly speaking, embraces the entire field of secret writing, while that branch of the subject dealing with the solution and reading of cryptic messages is generally referred to as cryptanalysis. ”

“ It is expected that the enemy will intercept dozens, and even hundreds, of cryptograms in a single day, some of which will inevitably be enciphered with the same key. With so much material, knowing the general subject matter, and often exactly what words to expect, or the personal expressions invariably used by individuals, it is conceded that he will read the messages. All that is desired of a cryptogram is that it will resist his efforts for a sufficient length of time to render its contents valueless when he finally discovers them. ”

“ Any one of the multiple-alphabet ciphers may change keys at each new group instead of with each consecutive letter. As a rule, this kind of encipherment is never found except in connection with very simple ciphers, and the intact plaintext groups, each one standing on its own key-line, are readily discovered by the decryptor who takes the precaution of cutting out a segment from his cryptogram and “running down the alphabet,” first treating the original letters and then, if necessary, their complements. ”

“ Decryptment, too, can parallel that of the Vigenère: The period of a cryptogram can be found through repeated sequences, or, in their absence, through repeated single numbers, and individual frequency counts can be taken on the several alphabets of the period. If the arrangement of letters in the checkerboard is that of the figure, or any other strictly alphabetical one to which the order of the numbers can be adjusted, these frequency counts will all follow the graph of the normal alphabet, with allowance made for the missing letter. ”

“ A factor of particularly grave importance in the selection of a cipher to fit a given purpose is the probable amount of enciphered material which is going to fall into the possession of unauthorized persons. A criminal, who has had to send but one brief cryptogram in a lifetime, might reasonably expect that it will remain forever unread, no matter how weak the cipher. A commercial firm, transmitting thousands of words over the air, is more vulnerable ”

“ A key-word, treated in the same way, is repeated often enough to pair one key-number with each message-number, and the final cryptogram is formed by adding these pairs of numbers. Decipherment, of course, will be the subtraction of key-numbers from the finished cryptogram and the resubstitution of letters. We have, then, another periodic cipher, not essentially different from those already seen. Any number in the checkerboard can become a key, to be applied periodically at some given interval, and thus may govern one of the 25 possible cipher alphabets. ”

“ But key-lengths are hardly ever shorter than 5, or as long as 18. He would seize upon the square as the object of his first investigation, writing the cryptogram into that block by various known routes, and also reading by various known routes, diagonally, horizontally, vertically, backward, or upside down, until he begins to find words. As a rule, this does not take him very long; often the very efforts of an encipherer to achieve complexity will result in an easier task for the decryptor. However, a spiral will sometimes give trouble. ”

“ It becomes possible, for many purposes, to make use of a cipher in which a single cryptogram, though probably read in the end, will resist the decryptor for the necessary length of time, several hours or several days. The double columnar transposition can be very resistant, especially when the key is long and the columns short, and can be made even more complicated by carrying it through still a third block, perhaps using a different key with each new block. ”

“ Usually time is saved by taking cryptogram pairs just as they come and filling in as many letters as possible; in this way, patterns are sometimes brought out, and thus we come back to step 1: the identification of more pairs. With the key-square beginning to shape up, the “chart of probable position” may be used to good advantage. For instance, what about the letters H and B which were very high in the frequency list?
Once a beginning is made, the cipher is broken, though just how rapidly we may proceed with the solution depends chiefly upon the manner in which the square has been filled. ”

“ The experienced solver knows well that persistence will find this entry, and trusts largely to instinct and perseverance; the beginner, however, may feel at a loss for a “system,” and, if so, may, perhaps, be able to find suggestions for one in the next few paragraphs.
First of all, in any substitution problem, there should be a counting of the letters in the cryptogram in order to find out their frequencies. This is called a frequency count, and is usually accomplished as follows: The decryptor first lays out the normal alphabet — either horizontally or vertically. ”

“ Transposition has already been explained as a form of cipher in which the letters of a message are disarranged from their natural order in accordance with any pattern, or key, agreeable to the correspondents. The fact that any plan may be followed will suggest the possible ramifications as to detail. Transpositions are, in fact, found in every conceivable degree of complexity. They are not even unanimous in their demand that there be two separate operations in the preparation of a cryptogram: (1) the writing down of the plaintext letters, and (2) the taking off of these letters. ”

“ Complete-unit ciphers, of course, may be troublesome, but their complexities are necessarily confined to one small area. An irregular cipher, on the other hand, usually involves the entire text, and its complexities may be real. In this class we occasionally find ciphers in which a single cryptogram is impossible to break; and we find others in which the eventual solution of one cryptogram will not instantaneously provide the key to another enciphered exactly like it. ”

“ Perhaps he has then marked his cryptogram into pairs of numbers or letters, and finds that these, also, are not likely to furnish the kind of frequency count which betrays simple substitution or some other cipher with which he is familiar. At this point, he is likely to pause and consider the source of the cryptogram. Is this the work of an expert, or the work of an amateur? Is it worthwhile to make up the statistics? ”

“ When this cipher is used for puzzle purposes, as we find it in our newspapers and popular magazines, the substitutes (which are invariably letters of the alphabet) may be chosen at random, and the cryptograms must follow certain arbitrary rulings which are designed to make them “fair”: Word-divisions and punctuation must follow religiously those of the original text; a certain minimum of length must be provided; no letter may act as its own substitute; foreign words are not permissible ”

“ But before entering into the subject of decryptment, let us look carefully at the system itself.
Primarily, we have a fixed substitution. No plaintext pair ever has more than one substitute pair; and no substitute pair ever changes its original. We might say that the Playfair is, in effect, a “simple substitution” based on an “alphabet” of 600 pairs; and, just as in simple substitution proper, the Playfair cryptograms will very often contain long repeated sequences which represent whole words. ”

“ With several alphabets in doubt, which could only happen when frequency counts are too scant to betray their graph, it might become necessary to decipher the periodic cryptogram with each possible [page 168] combination of key-numbers, each time obtaining a new cryptogram, and accept, among these new cryptograms, the one whose general frequency count seems most likely to be that of a simple substitution. ”

“ As to how a type may sometimes be identified, the difference between the regular and irregular types is ordinarily suggested by the number of letters contained in the cryptograms. Irregular types, intended for practical purposes, are nearly always seen in complete five-letter groups, where the geometric cipher usually results in a broken group at the end of its cryptogram. This, of course, is never mandatory upon the encipherer; it merely happens because the only persons making use of such ciphers are those who do not realize the advisability of doing otherwise. ”

“ Decryptment, here, is merely a matter of trying out the known routes, and it would never be actually necessary to write out the entire forty-plus blocks, or even half of these, for any one rectangle. The decryptor begins by counting the letters of his cryptogram and factoring the number of these, to find out what oblongs are possible. A 36-letter cryptogram, for instance, might mean dimensions 6 x 6, or dimensions 4 x 9. ”

“ The term cipher implies a method, or system, of secret writing which, generally speaking, is unlimited in scope; it should be possible, using any one given cipher, to transform any plaintext whatever, regardless of its length and the language in which it is written, into a cryptogram, or single enciphered message. ”

“ We do not desire, however, to take off plaintext. And, to use this same key on a cryptogram, we should have to use it in the writing-in manner; that is, first lay out the series of key-numbers, and then, taking the cryptogram letters in their 1-2-3 order, place them, one by one, below their key-numbers. But once the plaintext has been restored, the plaintext letters (or columns) may also have serial numbers, and these new serial numbers, in the figure, have been added at the bottoms of the columns. ”

“ These pairs and their supposed originals are set together in such a way as to start the reconstruction of the key-square.
3. Substitutions are made on the cryptogram and further pairs are identified.
When probable words exist, the work of solution becomes more or less mechanical, as we shall see. At worst, we may begin at the beginning of the cryptogram and work straight through until we find the word. But very often, a really probable word is repeated, and even repeated more than once. In the latter case, we are sure to find the long repeated sequence in the cryptogram ”

“ The decryptor, hoping for the best, writes his cryptogram into a square (or series of squares) by straight horizontals and counts the vowels per horizontal line. If his block is wide, he may estimate the actual number of vowels represented by 40%; if it is narrow, he may only roughly approximate the number; but in either case what he hopes to see is evenness of distribution. More than half of his units must be exactly normal, and any which are not exactly normal must show the smallest variation possible. ”

“ Knowing that a great many letters are going to be enciphered by B, a great many others by E, and a great many others by D, and having no wish to preserve word-divisions, we begin by writing our plaintext into three columns (or by grouping it conveniently) , and then encipher at a single writing all of those letters which are to be enciphered by any one same key-letter. That is, we apply one cipher alphabet at a time, as first explained. The modern practice will also require that the cryptogram be taken off in five-letter groups, and that the final group be made complete. ”

“ Thus, the sentence given above yields a series 1, 3, 1, 2, 1, 4, 4, 1, 4. Using a biform alphabet, these are usually considered simply as odd and even; with a triform alphabet, some disposition must be made of numbers larger than 3.
The subject is fascinating, and the literature of cryptography is rich with examples. However, we need not delve further into what, after all, is only the stepchild of a legitimate science. The matter of telegraphic transmission alone will bar these ciphers for most general purposes, or the fact that a cipher once betrayed will never serve again. ”

“ But there is so little difference in the results of the two procedures that a decryptor may solve and read a cryptogram without learning which of the two was actually followed. Ordinarily, it is the simple operation which comes first, the writing in of intact units one after another. Sometimes the opposite is true, the operation of writing in being made very complex, so that the whole block is the unit, the taking off being done by simple rows or columns. Frequently both operations are complex. This kind of transposition belongs rather to the category of puzzles than to cipher ”

“ He may provide himself, also, with non-pattern lists, on which words have given lengths but contain no repeated letters; and with “transposal lists” containing pairs of words (as NIGHT and THING) which use the same letters but not in the same order. It is true that such lists are troublesome to prepare, but they are extremely effective; they will break the most resistant of the “aristocrats” or the shortest example of legitimate cipher.
No matter how resistant the cryptogram, all that is really needed is an entry, the identification of one word, or of three or four letters. ”

“ But it is still present; the most complex of ciphers has method of some kind, provided we can find it. Consider, for instance, the series of numbers, 11-8-25-6-3-21-19-16-5-14, which has been forming in Fig. 53. Examination here shows pairs of consecutive numbers, 11-8, 6-3, and 19-16, all having the same numerical difference of 3; that is, the plan of our present encipherment, whatever it is, has, on three separate occasions, caused some plaintext digram to appear in the cryptogram reversed, and with its letters three positions apart. ”