COMMUNICATION THEORY OF SECRECY SYSTEMS 



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end there are two information sources — a message source and a key source. 

 The key source produces a particular key from among those which are 

 possible in the system. This key is transmitted by some means, supposedly 

 not interceptible, for example by messenger, to the receiving end. The 

 message source produces a message (the "clear") which is enciphered and 

 the resulting cryptogram sent to the receiving end by a possibly inter- 

 ceptible means, for example radio. At the receiving end the cryptogram and 

 key are combined in the decipherer to recover the message. 



Fig. 1 — ^Schematic of a general secrecy system. 



Evidently the encipherer performs a functional operation. If M is the 

 message, K the key, and E the enciphered message, or cryptogram, we have 



E = f(M, K) 



that is £ is a function of M and K. It is preferable to think of this, however, 

 not as a function of tw^o variables but as a (one parameter) family of opera- 

 tions or transformations, and to write it 



E = TiM. 



The transformation Ti applied to message M produces cryptogram E. The 

 index / corresponds to the particular key being used. 



We will assume, in general, that there are only a finite number of possible 

 keys, and that each has an associated probability pi . Thus the key source is 

 represented by a statistical process or device which chooses one from the set 

 of transformations Ti , Ti, • • • , T,,, with the respective probabilities pi , 

 p2 , ■ ■ ■ , pm • Similarly we will generally assume a finite number of possible 

 messages Mi , M2 , • • • , Mn with associated a priori probabilities qi , q-i , 

 ■ ■ ■ , qn . The possible messages, for example, might be the possible sequences 

 of English letters all of length N, and the associated probabilities are then 



