book cipher, to which I have already alluded. In this, a code

dictionary is prepared in which every word likely to be used is printed, and the words are numbered consecutively 00000,
00001, ... up, if necessary, to 99999. Thus each word is
• Life of the Marquis of Worcester by H. Dircks, London, 1865. Worcester's system of shorthand was described by him in his Century of Inventions , London, 1683, sections 3, 4, 5.
+ Various systems, includinej those used in classical and medieval times, are described in the History of Shortiiand by T. Anderson, London, 1862.
422 CRYPTOGRAPHS AND CIPHERS [CH. XVIII
represented by a number of five digits, and there are 10*^ such numbers available. The message is first written down in words. Below that it is written in numbers, each word being replaced by the number corresponding to it. To each of these numbers is added some definite pre-arranged clue number — the words in the dictionary being assumed to be arranged cyclically, so that if the resulting number exceeds 10^ it is denoted onl}^ by the excess above 10\ The resulting numbers are sent as a message. On receipt of the message it is divided into consecutive groups of five numbers, each group representing a word. From each number is subtracted the pre-arranged clue number, and then the message can be read off by the code dictionary. If and when such a message is published, the construction of the sentences is usually altered before publication, so that the key may not be discoverable by anyone in possession of the code- book or who has seen the cipher message. This is a rule applicable to all cryptographs and ciphers.
This is a cipher with 10^ symbols, and as each symbol consists of five digits, a message of n words is denoted by 5n digits, and probably is not longer than the message when written in the ordinary way. Since however the number of words required is less than 10^ the spare numbers may be used to represent collocations of words which constantly occur, and if so the cipher message may be slightly shortened.
If the clue number is the same all through the message it would be possible by not more than 10^ trials to discover the message. This is not a serious risk, but, slight though it is, it can be avoided if the clue number is varied; the clue number might, for instance, be 781 for the next three words, 791 for the next five words, 801 for the next seven words, and so on. Further it may be arranged that the clue numbers shall be changed every day; thus on the seventh day of the month they might be 781, 791, &c., and on the eighth day 881, 891, &c., and so on.
This cipher can however be further improved by inserting at some step, say after each mth digit, an unmeaning digit. For example, if, in the original message written in numbers, we
CH. XVIIl] CRYPTOGRAPHS AND CIPHERS 423
insert a 9 after every seven digits we shall get a collection of words (each represented by five digits), most of which would have no connection with the original message, and probably the number of digits used in the message itself would no longer be a multiple of 5. Of course the receiver has only to reverse the process in order to read the message.
It is however unnecessary to use five symbols for each word. For if w^e make a similar code with the twenty-six letters of the alphabet instead of the ten digits, four letters for each word or phrase would give us 26^ that is, 456976 possible variations. Thus the message would be shorter and the power of the code increased. Further, if we like to use the ten digits and the twenty-six letters of the alphabet — all of which are easily telegraphed — we could, by only using three symbols, obtain 36^ that is, 4G656 possible words, which would be sufficient for all practical purposes.
This code, at any rate with these modifications, is unde- cipherable by strangers, but it has the disadvantages that those who use it must always have the code dictionary available, and that it takes a considerable time to code or decode a com- munication. For practical purposes its use would be confined to communications which could be deciphered at leisure in an office.
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