Helen Gaines

“ But assuming a case in which we have no repeated sequences at all, we almost never meet with a Vigenère cryptogram in which there are no repeated single letters belonging to a same cipher alphabet. These repeated single letters can be tabulated with their separating intervals, and these intervals factored in exactly the same way as intervals between repeated sequences. The evidence, perhaps, will be less clear, and less reliable, than that obtained through repeated sequences; as with sequences, the less frequent letters will usually be more informative than those which are leaders. ”

“ 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. ”

“ One great objection to any device offering optional substitutes is that the encipherer himself seems unable to take full advantage of his system. Even having at his disposal five different substitutes for E, he falls into the habit of using one of these in preference to the other four; or, determined to avoid this, he uses them meticulously according to rotation, so that when a frequency chart is prepared from his cryptograms, this chart, which is, after all, a graph, will show the five uniform frequencies sticking out like a sore thumb. ”

“ Naturally, there are times when the matching of the columns, for one reason or another, proves troublesome. We are thrown off by errors, by the presence of nulls, initials, abbreviations, etc., or by the encipherer’s use of cover-up devices, such as the writing of YH instead of TH. Or we find that the handling of many paper strips, caused by message length, is awkward and confusing. But if, in the eyes of the decryptor, there is any good reason for finding out the contents of such messages, he can always succeed, even with only two letters per column. ”

“ The subject which we are about to study is the analysis and solution of cipher, though not including code, which is a very special form of cipher demanding something more than elementary knowledge; nor shall we enter at all into the subject of invisible inks, certainly a most important aspect of secret writing, but belonging to the province of chemistry rather than to that of cryptanalysis. Cipher machines, also, are not within our present scope. ”

“ When the alphabet of the square is an unknown mixed one, the problem may vary according to length, and the number of key-combinations which are found to be possible. If, for instance, the case resembles that of our preceding cryptogram, where only one alphabet out of four was in doubt, then, remembering that the Nihilist cipher alphabets are of a kind whose frequency counts can be “lined up,” we might take frequency counts on the several alphabets, and supply the missing numbers of the doubtful one by making its pattern match that of the rest. ”

“ Even a basically weak cipher, in the hands of an expert, can be made to serve its purpose; and the strongest can be made useless when improperly used.
In the present text, we are likely to be found looking at ciphers largely from a military angle, which, apparently, has a more general interest than any other. In time of war, the cryptographic service, that is, the encipherment and transmitting service, is suddenly expanded to include a large number of new men, many of whom know nothing whatever of cryptanalysis, or the science of decryptment. ”

“ For any cipher whatever in which the substitutes are two-digit numbers, a frequency count taken in chart form is usually far more convenient than one made by listing the numbers in advance. With only the ten digits, the 100 cells can be made larger than the 676 cells needed for letters, and the chart still be small and compact. The pairs of digits would be counted in exactly the same way as so many digrams. With numbers, it is sometimes possible to take the subsequent digram count, also, on a chart. Solution, in many cases, involves pure guess-work. ”

“ 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. ”

“ With a text of reasonable length, say 150 letters, it is sometimes possible to determine with certainty just which of the cryptogram-letters represent the six vowels; with shorter cryptograms, we can usually find four; sometimes only three. But once the separation has been made, individual vowels can usually be established as follows:
The most frequent one is ordinarily E. The one which never touches it is most likely to be O. Both of these are very freely doubled, and for that reason are often confused with each other, but seldom with any other vowel. They rarely touch each other. ”

“ Certain letters, ordinarily those of lowest frequency, are peculiar in their contacts with other letters. The shining example, in most languages, is the letter Q, followed, almost 100% of the time, by U plus another vowel; and if it seems, in the present text, that the significance of QU is being overlooked, this is simply because the individuality of this digram, like that of the German CH (CK) , is so well advertised that even the novice encipherer finds a way to avoid using it. It is impossible, however, to avoid all letters having individual preferences. ”

“ The members of the American Cryptogram Association, who solve a great many Vigenères, Beauforts, and so on, as a matter of recreation, have practically all “invented” slides (or tableaux) which will, to some extent, do away with the irksome task of carrying out a trigram-search. These are prepared in various ways, and variously used, though the principle for all is about the same as that indicated in Fig. 114. They are usually referred to as decrypting slides, and the single stationary alphabet, sometimes a list of key-letters and sometimes not, will be called “the decrypting alphabet.” ”

“ Experience counts for most, and extensive reading is a vast help. Having seen methods in use, or read the descriptions of methods, we know of some definite thing to look for. Then, too, some of the concealment ciphers have transposition characteristics. This would be the case with the Legrand cipher, which is of the type called “open letter.”
This cipher used a numerical key, which, in turn, was based on a keyword in what seems today a rather odd manner: A keyword CAT, made up of the 3d, 1st, and 20th letters of the alphabet, gives the key 3 1 2 0. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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? ”

“ Vowels do not often contact one another. If the letter of highest frequency can be assumed as E, any other high-frequency letter which never touches E at all is practically sure to be another vowel, and one which contacts it very often cannot be a vowel. ”

“ Trigrams, tetragrams, and other polygrams, found in alphabet squares, can always be considered as geometrical figures, and replaced with other series of letters in related geometrical figures; and Lester S. Hill, in the American Mathematical Monthly, has described an “algebraic” method which appears practical, provided a machine is used. These methods, however, even
granting that some are practical and not too unwieldy for use, are entirely beyond our present scope, and we will spend our few remaining pages on a cipher of a less cumbersome nature and presenting far more points of interest. ”

“ The matching of strips is generally a purely mechanical process, in which impossibilities are not considered. However, having before us a block (a) or (b) , it is possible to apply the principle used with our former digram VI, and find out in advance whether certain letters found on two strips can possibly have stood in sequence. Nor is the cutting apart of the strips really necessary; it is merely a convenient method for dispensing with mental effort.
Now suppose we consider this same cryptogram on the theory that its key-length cannot be determined, or restricted to certain possibilities. ”

“ After one grows accustomed to the swastika-like route of the open cell, such indices are not at all difficult to prepare at the moment of need; however, many solvers prefer to make them up in sets, once for all, and have them ready as they happen to be wanted. As to the finding of the four letters per block which follow any one index, it is sufficient to remember that the cell numbers, arranged in the manner shown, are also the serial numbers of the letters belonging to any one unit. ”

“ It is never a bad idea, in a puzzling example, to make the various digram-counts (in chart form) : An actual digram count, in which every letter is considered the beginning of a digram; a pair-count on separated pairs, as in Playfair; the two counts which could be made with the cryptogram marked off into three-letter groups; and the kind of pair-count which could be made in Playfair if the first cryptogram-letter were omitted. Many devices, as mentioned, may be uncovered simply by “running down the alphabet.” ”

“ Now, consider the true Beaufort cipher: Here, plaintext letters are found first, and keys are found by tracing into the square, so that encipherment is more or less a letter-by-letter process, and hardly so convenient as in the other two ciphers. It is true that every ascending diagonal in the tableau is made up of only one key-letter, so that a ruler, laid diagonally across this tableau, will point out a whole line of C’s, or O’s, or M’s. ”