Chapter XIII
_Le Chiffre Indechiffrable_
During the world war I had been on duty in the intelligence department,and I had taken much interest in the science of cryptography, althoughnot connected personally with the handling of cypher despatches. I couldtherefore explain to Betty that cypher systems fall under four generalheads.
1. The giving to words, or groups of letters, a purely arbitrarysignificance.
2. The use of mechanical transformers in the shape of a screen or grid.
3. The substitution of numbers or other symbols for the originalcharacters.
4. The transposition of letters according to a constant formula.
"Obviously," I began, "the example before our eyes--long lines ofletters without breaks or marks of punctuation--does not come under thefirst heading. It contains no recognizable words, or phonetic groups,which might correspond in the code book to actual sentences. Forexample, in the ordinary commercial systems, the word _Barbarian_ maymean: 'The wheat market is advancing.' But if I cable the word_Civilisation_ I really intend to say: 'Australian wool crop is afailure.' The principal value of the elaborate code system is in thesaving of cable tolls, a single word conveying the meaning of an entiresentence. It is necessary, of course, that all of the correspondentsshould possess individual copies of the code, and loss or theft of thebook discloses the whole secret. Do you understand?"
Betty thought she did, and seemed so interested that I was emboldened toassume my best lecture manner.
"Under the second head we may consider the mechanical device known asthe 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 thepaper, and marks in the letters making up the words of his despatchthrough the apertures. Then the screen is removed, and the blank spacesare filled up with writing which has nothing to do with the real subjectmatter, the process being repeated until the entire message has beencoded. The recipient is provided with a precisely similar grid. Byapplying it to the communication he is then able to read, through theholes, the text of the secret message. The ancient Romans used avariation of this method, somewhat as follows. A long strip of paper waswound spirally about a cylinder or cone; the writing was then doneparallel with the axis of the metal form. When unrolled, thecommunication seemed to be made up of arbitrary signs really parts ofletters which were entirely unintelligible. The recipient, however, byrewinding the strip on a precisely similar form, would be able to readthe message.
"Of course we may rule out the mechanical device. In this case we have along communication of several hundred words, and the grille would beimpracticable--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 puresymbols--stars and daggers or what not. The latter variation isgenerally 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 isrepresented by a group of five numbers, two designating the location ofthe required word on the page, and the remaining three denoting thenumber of the page itself. The process, both of coding and of uncoding,is very laborious, and hardly pays for the trouble involved. Another wayto use the two dictionaries is to interpret the words of the codemessage by substituting other words removed a certain definite distanceup or down the column. Suppose it is agreed that 'fifteen down' shall bethe key, and that the despatch, as received, reads: _Bull Collier_. Therecipient 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 lettergroups, and work out an intricate transposition, reversing the processin 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 asystem of the fourth order in which the letters are transposed accordingto a constant prearranged formula.
"Let us first consider the simple form; the regular substitution of oneletter of the alphabet for another. For example, X always takes theplace of E, while B invariably means T, and so on. Such cyphers areeasily read by the expert, who works on the principle that all theletters of the English alphabet may be ranked on a numerical scale ofaverage frequency in use. The letter E heads the list; consequently, ifany particular symbol predominates in the message it must correspond tothat hard-worked vowel. Again, as _the_ is the commonest word group inthe 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 mayeffect a transposition of letters, the substitution being variable orirregular. For instance, the 'Checkerboard,' invented by the Russiannihilists, and similar devices, most of which depend for secrecy uponsingle or double key-words. Perhaps the cleverest system in this groupis the cypher called by the French, 'Le Chiffre Indechiffrable.'"
"'The Undecypherable Cypher,'" commented Betty. "Sounds ratherhopeless."
"Well, you can decide for yourself if there is any reasonablepossibility of unravelling it, unless you are lucky enough to stumble onthe key-word."
"Try me," she challenged.
"To begin with, you write down the twenty-six letters of the Englishalphabet in a horizontal line, indenting it the space of a singleletter."
"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 differencebeing that all these other lines begin at the left-hand margin, eachwith a different letter in their strict alphabetical order. Yourdiagram will then look like this. For the present I am putting it inskeleton 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'ssake, we'll take the short word: BEAD, and suppose we wish to send incypher the message: CAB FEED."
"Which is pure nonsense."
"Granted. I merely select two words at random which can be coded on myincomplete square. If I had the whole diagram drawn out the messagecould 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, inthe top horizontal line; and C, the first letter of the word to be putinto code, in the left-hand vertical line. Now look for the letter atthe intersection of the vertical column headed by B and the horizontalline which C begins. You will find it to be E. Set this down as thefirst symbol of your cypher message, and obtain the other letters in asimilar manner. Your despatch will then read: E F C J G J E. As anobject lesson, place these letters under your original arrangement ofkey-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. Forexample, the symbol E stands for both C and D. Again, the letter E inthe 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, andabove 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 thesymbol letter E; then move your pointer over left to the end of thathorizontal line which will give you C, the first letter of the originalmessage. Understand?"
Betty tried her hand, and quickly caught the trick; really it was veryeasy.
"One more point; it is better not to divide the cypher message into wordgroups as the continuous string of letters looks more mystifying. Thereis no difficulty in picking out the sense when decoding."
"Finally, you notice that the upper left-hand space in the diagram isvacant; consequently you must not use the letter Z in either thekey-word or in the message to be coded. But this restriction is not ofany practical disadvantage, Z being a letter that is seldom used. Itwill 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 thecomplications are absolutely overwhelming."
"And you can make them still more intricate by merely using a longerkey-word, or indeed a whole sentence. For example: 'I love BettyHildebrand.'"
"Everybody knows that," retorted Betty. "Still I don't mind anoccasional restatement of the established fact. Please, Hugh! I spentany amount of time in getting those ruffles starched just so."
Betty took the diagram and carefully tucked it away in a drawer of hersecretary. "Of course we can't be sure that old Mr. Thaneford reallyused 'Le Chiffre Indechiffrable,'" she said thoughtfully.
"Only a possibility," I agreed.
"And without the key-word or key-sentence we shall never be any wiserthan we are."
"Granted again."
"So there you are. Just the same, Hugh, I wish you would make me acomplete 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 hourto draw out the diagram in full; then I had to mount it on cardboard soas to keep it in good condition for constant handling. For the benefitof the curious-minded I reproduce it below:
LE CHIFFRE INDECHIFFRABLE
----------------------------------------------------- | |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 usingthis particular cypher system, it has no value in itself; the wholesecret depends upon the possession of the key-word or key-sentence. Asthis may easily be memorized by the two correspondents there is no riskof discovery through the accident of loss or theft.