One of the earliest cipher methods is recorded by Herodotus, was shaved, and the message tattooed on his scalp. After his hair had grown, he was sent on his way. When he reached his destination his head was again shaved, and the message read.
This article must be in part a taking of time-out to offer something besides thanks to the many who have sent in messages to be deciphered. The thanks are there, and deeply expressed; but with them there must go a word of criticism, to wit: several messages which entirely defied my best efforts proved, on consulting the enclosed key, to be undecipherable even with the full directions in view!
I have in mind particularly one most tantalizing array of figures: it ran something like this: 3158742785183775492, etc. It contained a prime number of figures, so that it could not be broken up into groups for possible addition; there seemed to be no recurrences, though there were a few promising-looking doubles. Now logic will show that it is impossible to make a substitution alphabet using single figures for letters, as there are only 9 figures — or 10, if you count zero — whereas there are 26 letters.
One of the elemental laws of cryptogram-deciphering is that when one finds a message composed wholly of figures those figures must be in combination, in some way or other.
Well, in this particular message, in despair I opened the sealed key, and found that the contributor had made two circles of cardboard, each divided into 9 parts and turning on a common center. In the inner circle were written the numbers from 1 to 9, in scrambled order; in the outer was the alphabet, in nine groups of three letters each, except one, which contained only two letters. To code, the inner circle was placed in one position, and the required letter was given the number that happened to come under it; then the outer circle was moved clockwise one space, and the second letter coded by its figure; and so on.
The worst of it was that even with the key and full directions it was impossible to decode the message!
The first figure was 2; it was under the division containing the letters DEF. How could I — or anyone else — know which of the three letters was the right one? The second figure was 7, and fell under PQR; what help was there? One might guess that R, as a common letter, was the second letter of the message; but a word could begin with DR, ER, or FR; moreover EQ could have been a perfect beginning — EQUAL, for instance; and the farther one went, the more tangled the whole thing would be. So let me stress a point once more:
A code to be of any use at all must be practical.
Nothing would be more easy than to compose a code which I could not decipher; in fact, there are plenty of straight codes which I should hate to tackle without unlimited time at my disposal; but there is always the danger that in being extremely secretive the composer will be so secretive that he will fool everyone, including the recipient of his message. Obviously a method of secret communication must be open to the holder of the key, or it becomes useless.
This is, of course, the basis for the original claim that what one man can invent another can decipher. It is presupposed that with the key the message can be read; the job of the decipherer is to find the key.
Having pushed which out of our system, let us return to more practical matters.
Enough, it seems to us, has not been made of the so-called “Dictionary” ciphers, or “Book” ciphers. This is a very simple method, easily disguised and difficult of decipherment. The method of coding is easy: a book — usually a small dictionary — is agreed upon between the parties; the message is coded by taking words — not letters — from the book and sending a series of numbers to indicate the page and the location of the word on the page. In the case of a dictionary, in which the words would be arranged in columns, three numbers usually represent the words — page, column, and position in the column. The small pocket dictionaries, which contain from fifty to a hundred thousand words, are excellent for this purpose.
I have, let us say, such a dictionary, containing 400 pages. I wish to send the message “If you will meet me at one o’clock I will tell you everything.” I search for the word “If,” and find it to be the fifth word from the top in the second column on page 147. I write 5-2-147, and proceed to “You.” This is the eighth in the first column on page 397, and is coded 8-1-397. “Will” occurs as 11-2-306, “Meet” as 16-1-201, “Me” as 22-2-200, “at” as 11-2-16, and so on. These are actual codings, by the way, from a real book. The message is sent like this:
52147 81397 112306 161201 222200 112016, etc., etc.
Note that in the last number the page — 16–was given a zero in front of it. This was so that the recipient of the message would not imagine, as he might, that the word was the first word in the first column on page 216, as it would seem if written 11216. The receiver takes the last three figures of each number, which gives him the page; the next figure is the column, and the first figure or figures the word itself.
How can such a message be decoded?
There are several tables which give the proportion of words in dictionaries according to their initials; the alphabet itself is a fairly good guide. Thus M is the middle letter of the alphabet, and M falls nearly in the middle of any dictionary. A is, of course, at the beginning, and Z at the end; the other letters fall pretty much where you would suppose. If you open a dictionary three-quarters of the way from the beginning you will land in the S’s, almost certainly.
It is unlikely that a dictionary used for coding will have pages numbered in more than three figures. A book of over 1,000 pages would be bulky to handle and would contain far too many useless words. Assuming that the dictionary is small, the first task of the decoder is to try to find the numbers which represent the pages. Remember that in a message of any length the same words are certain to crop up — AND, OF, WITH, etc. We omit THE because it is probable that such a message would omit this word, as is done in telegraphing. If, however, the decoder found several numbers which were very small he would be justified in assuming that these represented words beginning with A; and if the same numbers were repeated it would be a sure sign that they stood for common A-words like AND, AT, AM, ARE. Repeated words with very large numbers would be near the end of the dictionary — probably YOU or YOUR. Note in our own message, also, the consecutive page-numbers 201-200. In a 400-page book these would be about the middle — M-words — and the fact that they were so close together would suggest some such combination as MEET ME.
We are aware that this sounds like rank guesswork; and we admit at once that the solving of Dictionary ciphers involves the least straight reasoning and the most assumption. There are ways of scrambling the numbers, too — for instance, the first two and the last figure might represent the page, the second one or two the number of the word, and the remaining figure the column. To code Word 14, column 2, page 363, we would write 36-14-2-3, only of course the hyphens would be omitted–361423. Not an easy task for a would-be decoder!
The difficulty with dictionary codes is the likelihood of getting the figures so scrambled that the receiver, even with the key, may be led astray. He might even confuse BUY with SELL, which could be highly disastrous. In the effort to insure understandability certain give-aways are likely to crop up; for instance, few small dictionaries have more than two columns to the page; the decoder, noticing that 1 or 2 is always in the same place in each number, receives a strong hint. Even if the columns are not indicated there is bound to be a series of numbers running regularly from small to large, which will furnish a clue.
Andre Langie, the French cryptographer, tells of deciphering a dictionary-coded message from which he obtained the meaning “Either X or Y warmly recommended.” The actual meaning of the message, it developed, was “Both X and Y absolutely unknown!” The numbers had been skilfully scrambled so as to lead the solver far astray. This, however, could hardly be done in a message of any length.
We recommend dictionary codes to our readers as simple and certain, as well as difficult to decipher.