Cryptogram

“ Thus, when we find, in the present cryptogram, that the numbers 02, 53, and 63, have each a frequency of 2, it seems reasonable to suppose, for each number, that its two occurrences were in a single cipher alphabet; that is, that each one is a periodic repetition. Now, considering Fig. 133, and confining our observations, for the moment, to the number 02, we find that this number, in the cryptogram, occupies serial positions 49 and 154. Having first laid out a series of columns headed by the various possible periods, 2, 3, 4, 5. ”

“ Thus, there is never a time when it is impossible to see the tens and units as having been separately added; if we find, in a Nihilist cryptogram, the two numbers 29 and 87, with a difference greater than 4 in their respective tens-digits, we may say promptly that they were not enciphered with the same key; no digit whatever added to any two digits of the original square can produce a difference greater than 4. But if the two cryptogram numbers are 30 and 77, where the difference in the tens-digits appears, at first glance, to be only 4, the presence of the zero must be taken into account ”

“ The recipient of the present cryptogram, for instance, finds nine letters, divides this number by 3, thus ascertaining that three columns were used, covers up the other nine columns, then, proceeding by straight horizontals, places one cryptogram-letter wherever he sees a hole. Having thus restored all letters to their proper columns, he has the plaintext message before him. It will be noticed that an encipherer uses only the number of columns that he needs. His last column does not have to be completed with nulls, as in the case of complete-unit ciphers. ”

“ 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. ”

“ 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. ”

“ It is impossible to avoid every characteristic of the English language and still write English.
[page 77] The General Case. — Now let us examine carefully Fig. 64, where the foregoing cryptogram is repeated without its word-separations, and is followed by its frequency and contact data. The various devices indicated in this figure are all of a more or less optional nature. Concerning the preparation of the cryptogram itself, the chief requirement is that it be done in ink, or typewritten, on paper which
will suffer a great deal of erasure. ”

“ It is quite possible, and frequently happens, that one is able to reconstruct the particular system of secret writing from which a cryptogram has been constructed, and then fail to find the key. A really scientific cryptogram never leaves the key to guesswork, but gives a carefully hidden clue for the finder to work upon; because most cryptograms are intended to be solved, and if the composer of the message left its discovery to guesswork he would be defeating his own ends. ”

“ 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. ”

“ 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.” ”

“ 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 ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Some solvers do not prepare an alphabet in advance, but simply put down the main letters as they happen to come across them in the cryptogram. It should be added, too, that the few contacts included in Fig. 63 were taken from the undivided cryptogram. When word-divisions exist, and are known to be the correct ones, a great many solvers do not include any contacts which involve two different words. ”

“ 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. ”

“ While we do not often encounter doubled [page 90] letters in this form of cryptogram, it may be well to say here that while a doubled letter would be counted among the frequencies of letter appearance, its contacts with itself would not be entered on the consonant-line. That is, a doubled L would add a frequency of 2 to the general count, but contacts L-L would be ignored. ”

“ 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. ”

“ Those which are shorter will give more trouble; but it takes a very short cryptogram indeed to be really resistant.
Our foregoing cryptogram contains only 80 letters.
To apply “pointers” in this case, let us begin by considering the individual frequencies of the letters E T A O N I R S H. Their frequencies per 100, according to our own chart, are about as follows: E, 12; T, 10; A, 8; O, 8; N, 7; I, 7; R, 6; S, 7; H, 5. Thus, when frequency alone is considered, E and T have a tendency to draw away from the others and form a private high-frequency group of their own. ”

“ 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. ”

“ 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. ”

“ 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 ”

“ The Vigenère cipher, and, in particular, the Kasiski method of solution, have given rise to much research among members of the American Cryptogram Association. We doubt that any of this research has ever resulted in any new or valuable discovery. Yet it is interesting in that it shows a body of amateurs arriving at devices which are fully as effective or convenient as those proposed by seasoned cryptanalysts. ”

“ 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. ”

“ 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. ”

“ This does not mean that all repeated sequences found in Vigenère cryptograms are periodic. Often, they are purely accidental; oftener still, they will be due to the repetition of alphabets in the key itself, especialiy if it is such a word as CORCORAN or DESDEMONA. But a distinct majority of them, according to Kasiski, are caused by periodicity; and if all of the repeated sequences found in a given cryptogram be examined to find what the separating interval is in each case, and if all of these intervals be factored, the factor which predominates will betray the period of the cryptogram. ”

“ But it is very seldom indeed that a series of cipher alphabets used in the same cryptogram will be unrelated alphabets. Nearly always, they will have resulted from the use of a slide, and when this is true, the recovery of alphabets and parts of alphabets enables us to reconstruct the slide. The usual plan for recording substitutes is to lay out a plaintext alphabet in A B C order and then, directly below it, to rule off several rows of cells, one row for each cipher alphabet. ”