Chapter XIII

_Le Chiffre Indéchiffrable_

During the world war I had been on duty in the intelligence department, and I had taken much interest in the science of cryptography, although not connected personally with the handling of cypher despatches. I could therefore explain to Betty that cypher systems fall under four general heads.

1. The giving to words, or groups of letters, a purely arbitrary significance.

2. The use of mechanical transformers in the shape of a screen or grid.

3. The substitution of numbers or other symbols for the original characters.

4. The transposition of letters according to a constant formula.

"Obviously," I began, "the example before our eyes--long lines of letters without breaks or marks of punctuation--does not come under the first heading. It contains no recognizable words, or phonetic groups, which might correspond in the code book to actual sentences. For example, in the ordinary commercial systems, the word _Barbarian_ may mean: 'The wheat market is advancing.' But if I cable the word _Civilisation_ I really intend to say: 'Australian wool crop is a failure.' The principal value of the elaborate code system is in the saving of cable tolls, a single word conveying the meaning of an entire sentence. It is necessary, of course, that all of the correspondents should possess individual copies of the code, and loss or theft of the book discloses the whole secret. Do you understand?"

Betty thought she did, and seemed so interested that I was emboldened to assume my best lecture manner.

"Under the second head we may consider the mechanical device known as the grid, grille, or screen.

"The instrument in question consists of a plate, usually made of metal, pierced by a number of holes of different sizes and irregularly spaced. When the writer sets out to prepare his message he lays the grid on the paper, and marks in the letters making up the words of his despatch through the apertures. Then the screen is removed, and the blank spaces are filled up with writing which has nothing to do with the real subject matter, the process being repeated until the entire message has been coded. The recipient is provided with a precisely similar grid. By applying it to the communication he is then able to read, through the holes, the text of the secret message. The ancient Romans used a variation of this method, somewhat as follows. A long strip of paper was wound spirally about a cylinder or cone; the writing was then done parallel with the axis of the metal form. When unrolled, the communication seemed to be made up of arbitrary signs really parts of letters which were entirely unintelligible. The recipient, however, by rewinding the strip on a precisely similar form, would be able to read the message.

"Of course we may rule out the mechanical device. In this case we have a long communication of several hundred words, and the grille would be impracticable--too wasteful of space."

"That disposes of No. 2," said Betty hopefully. "What next?"

"In class 3 the coded message consists of numbers, or even of pure symbols--stars and daggers or what not. The latter variation is generally pure substitution, and may be called kindergarten cryptology. No one but a rank amateur would employ such a system.

"In the numeral code each correspondent is supplied with a dictionary, the same edition of course. Each word of the original message is represented by a group of five numbers, two designating the location of the required word on the page, and the remaining three denoting the number of the page itself. The process, both of coding and of uncoding, is very laborious, and hardly pays for the trouble involved. Another way to use the two dictionaries is to interpret the words of the code message by substituting other words removed a certain definite distance up or down the column. Suppose it is agreed that 'fifteen down' shall be the key, and that the despatch, as received, reads: _Bull Collier_. The recipient takes his copy of the dictionary, looks up the word _Bull_, and counts down fifteen, getting the word _Buy_. Similarly, _Collier_ gives him _Copper_, and the decoded message will mean: 'Buy copper.' Finally, we may use a predetermined series of numbers as a key formula. We then divide the message to be coded into the same number of letter groups, and work out an intricate transposition, reversing the process in order to decode."

"Rather makes your head ache," remarked Betty plaintively. "Besides, this cypher doesn't use numbers at all."

"Right you are," I acquiesced, "and we are undoubtedly dealing with a system of the fourth order in which the letters are transposed according to a constant prearranged formula.

"Let us first consider the simple form; the regular substitution of one letter of the alphabet for another. For example, X always takes the place of E, while B invariably means T, and so on. Such cyphers are easily read by the expert, who works on the principle that all the letters of the English alphabet may be ranked on a numerical scale of average frequency in use. The letter E heads the list; consequently, if any particular symbol predominates in the message it must correspond to that hard-worked vowel. Again, as _the_ is the commonest word group in the language we are quickly able to identify what stands for T and H. But this is quite too transparent a code for serious use."

"Then don't waste time over it," said my practical-minded wife. "Old Mr. Thaneford was not a foolish person."

I took a long look at the incomprehensible jumble of letters.

"There are any number of formulae," I went on, "by means of which we may effect a transposition of letters, the substitution being variable or irregular. For instance, the 'Checkerboard,' invented by the Russian nihilists, and similar devices, most of which depend for secrecy upon single or double key-words. Perhaps the cleverest system in this group is the cypher called by the French, 'Le Chiffre Indéchiffrable.'"

"'The Undecypherable Cypher,'" commented Betty. "Sounds rather hopeless."

"Well, you can decide for yourself if there is any reasonable possibility of unravelling it, unless you are lucky enough to stumble on the key-word."

"Try me," she challenged.

"To begin with, you write down the twenty-six letters of the English alphabet in a horizontal line, indenting it the space of a single letter."

"Indenting?"

"You'll understand when you see the diagram I'm preparing."

"Oh, you're making a magic square!"

"Yes. Now you repeat the process twenty-five times, the only difference being that all these other lines begin at the left-hand margin, each with a different letter in their strict alphabetical order. Your diagram will then look like this. For the present I am putting it in skeleton form:"

A B C D E F G.............W X Y A B C D E F G H.............X Y Z B C D E F G H I.............Y Z A C D E F G H I J.............Z A B D E F G H I J K.............A B C E F G H I J K L.............B C D F G H I J K L M.............C D E ................................. ................................. W X Y Z A B C D.............T U V X Y Z A B C D E.............U V W Y Z A B C D E F.............V W X

"Now choose a key-word, or preferably, a key-sentence. For simplicity's sake, we'll take the short word: BEAD, and suppose we wish to send in cypher the message: CAB FEED."

"Which is pure nonsense."

"Granted. I merely select two words at random which can be coded on my incomplete square. If I had the whole diagram drawn out the message could be anything you like."

"Go on," commanded Betty, her eyes snapping.

"First you write down your message; then above it you put the key-word, repeated in whole or in part as many times as may be necessary, thus:"

B E A D B E A C A B F E E D

"Turning to the diagram you find B, the first letter of the key-word, in the top horizontal line; and C, the first letter of the word to be put into code, in the left-hand vertical line. Now look for the letter at the intersection of the vertical column headed by B and the horizontal line which C begins. You will find it to be E. Set this down as the first symbol of your cypher message, and obtain the other letters in a similar manner. Your despatch will then read: E F C J G J E. As an object lesson, place these letters under your original arrangement of key-word and message, thus:"

B E A D B E A C A B F E E D E F C J G J E

"You see at a glance that the substitution is irregular and variant. For example, the symbol E stands for both C and D. Again, the letter E in the word F E E D is at one time represented by G and secondly by J."

"How do you translate the cypher?" asked Betty.

"Merely reverse the process. You write down the cypher message, and above it as many letters of your key-word as may be needed, thus:"

B E A D B E A E F C J G J E

"Now follow down the vertical column headed by B until you reach the symbol letter E; then move your pointer over left to the end of that horizontal line which will give you C, the first letter of the original message. Understand?"

Betty tried her hand, and quickly caught the trick; really it was very easy.

"One more point; it is better not to divide the cypher message into word groups as the continuous string of letters looks more mystifying. There is no difficulty in picking out the sense when decoding."

"Finally, you notice that the upper left-hand space in the diagram is vacant; consequently you must not use the letter Z in either the key-word or in the message to be coded. But this restriction is not of any practical disadvantage, Z being a letter that is seldom used. It will often appear, of course, in the cypher itself."

"Certainly it is all very simple," remarked Betty.

"But without the key-word where would you get off?"

"I don't see how anybody could possibly work it out; why the complications are absolutely overwhelming."

"And you can make them still more intricate by merely using a longer key-word, or indeed a whole sentence. For example: 'I love Betty Hildebrand.'"

"Everybody knows that," retorted Betty. "Still I don't mind an occasional restatement of the established fact. Please, Hugh! I spent any amount of time in getting those ruffles starched just so."

Betty took the diagram and carefully tucked it away in a drawer of her secretary. "Of course we can't be sure that old Mr. Thaneford really used 'Le Chiffre Indéchiffrable,'" she said thoughtfully.

"Only a possibility," I agreed.

"And without the key-word or key-sentence we shall never be any wiser than we are."

"Granted again."

"So there you are. Just the same, Hugh, I wish you would make me a complete diagram; I'd like to experiment with it."

"I'll do it for you to-night. Here's your precious diary."

Betty kissed me and went upstairs. It took me the best part of an hour to draw out the diagram in full; then I had to mount it on cardboard so as to keep it in good condition for constant handling. For the benefit of the curious-minded I reproduce it below:

LE CHIFFRE INDÉCHIFFRABLE

----------------------------------------------------- | |A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y| ----------------------------------------------------- |A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z| ----------------------------------------------------- |B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A| ----------------------------------------------------- |C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B| ----------------------------------------------------- |D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C| ----------------------------------------------------- |E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D| ----------------------------------------------------- |F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E| ----------------------------------------------------- |G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F| ----------------------------------------------------- |H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G| ----------------------------------------------------- |I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H| ----------------------------------------------------- |J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I| ----------------------------------------------------- |K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J| ----------------------------------------------------- |L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K| ----------------------------------------------------- |M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L| ----------------------------------------------------- |N|O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M| ----------------------------------------------------- |O|P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N| ----------------------------------------------------- |P|Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O| ----------------------------------------------------- |Q|R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P| ----------------------------------------------------- |R|S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q| ----------------------------------------------------- |S|T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R| ----------------------------------------------------- |T|U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S| ----------------------------------------------------- |U|V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T| ----------------------------------------------------- |V|W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U| ----------------------------------------------------- |W|X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V| ----------------------------------------------------- |X|Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W| ----------------------------------------------------- |Y|Z|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X| -----------------------------------------------------

Note that while the diagram is a necessary piece of machinery in using this particular cypher system, it has no value in itself; the whole secret depends upon the possession of the key-word or key-sentence. As this may easily be memorized by the two correspondents there is no risk of discovery through the accident of loss or theft.