306 CRYPTOGRAPHS AND CIPHERS [CH. XIV 



The clue number may be communicated indirectly in many 

 ways. For instance, it may be arranged that the number to 

 be used shall be the number sent, plus (say) q, or that the 

 number to be used shall be an agreed multiple of the number 

 actually sent. 



Third Type of Ciphers. Complex Shifting Alphabets. A 

 cipher of the third type is one in which the same symbol 

 represents sometimes one letter or word and sometimes 

 another. 



A simple example, known as Gronf eld's Method, is the employ- 

 ment of pre-arranged numbers in shifting forward the letters 

 that make the communication. For instance, if we agree on 

 the key number 6814, then the first letter in the communica- 

 tion is replaced by the sixth letter which follows it in the 

 natural order of the alphabet: for instance, if it were an 

 a it would be replaced by g. The next letter is replaced by 

 the eighth letter which follows it in the natural order of the 

 alphabet: for instance, if it were an a it would be replaced by i. 

 The next letter is replaced by the first after it; the next by 

 the fourth after it; the next by the sixth; and so on to the 

 end of the message. Of course to read the message the reci- 

 pient would reverse the process. If the letters of the alphabet 

 are written at uniform intervals along a ruler, and another ruler 

 similarly marked with the digits is made to slide along it, the 

 letter corresponding to the shifting of any given number of places 

 can be read at once. Here is such a message: — Cisvg vumya 

 vijnp vgzsi ybpjp woiy. Such ciphers are easy to make and 

 read by those who have the key. But in recent years their 

 construction has been subjected to critical analysis, and experts 

 now can generally obtain the key number if the message contains 

 80 or 100 words; an example of the way by which this is done is 

 given below. It would be undesirable to allow the division into 

 words to appear in the message, and either the words must be run 

 on continuously, or preferably the less common letters j, q, z 

 may be used to mark the division of words and the message 

 then written in five letter groups. 



It is most important to conceal the number of digits in the 



