CH. XIV] CRYPTOGRAPHS AND CIPHERS 319 



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 6 it is denoted only by the 

 excess above 10 6 . 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 6 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 6 , 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 rath digit, an unmeaning digit. 

 For example, if, in the original message written in numbers, we 



