Communication Theory of Secrecy Systems* 



By C. E. SHANNON 



1. Introduction and Suivimary 



THE problems of cryptography and secrecy systems furnish an interest- 

 ing appUcation of communication theory.^ In this paper a theory of 

 secrecy systems is developed. The approach is on a theoretical level and is 

 intended to complement the treatment found in standard works on cryp- 

 tography.- There, a detailed study is made of the many standard types of 

 codes and ciphers, and of the ways of breaking them. We will be more con- 

 cerned with the general mathematical structure and properties of secrecy 

 systems. 



The treatment is limited in certain ways. First, there are three general 

 types of secrecy system: (1) concealment systems, including such methods 

 as invisible ink, concealing a message in an innocent text, or in a fake cover- 

 ing cryptogram, or other methods in which the existence of the message is 

 concealed from the enemy; (2) privacy systems, for example speech inver- 

 sion, in which special equipment is required to recover the message; (3) 

 "true" secrecy systems where the meaning of the message is concealed by 

 cipher, code, etc., although its existence is not hidden, and the enemy is 

 assumed to have any special equipment necessary to intercept and record 

 the transmitted signal. We consider only the third type — concealment 

 systems are primarily a psychological problem, and privacy systems a 

 technological one. 



Secondly, the treatment is limited to the case of discrete information, 

 where the message to be enciphered consists of a sequence of discrete sym- 

 bols, each chosen from a finite set. These symbols may be letters in a lan- 

 guage, words of a language, amplitude levels of a "quantized" speech or video 

 signal, etc., but the main emphasis and thinking has been concerned with 

 the case of letters. 



The paper is divided into three parts. The main results will now be briefly 

 summarized. The first part deals with the basic mathematical structure of 

 secrecy systems. As in communication theory a language is considered to 



* The material in this paper appeared originally in a confidential report "A Mathe- 

 matical Theory of Crj^stography" dated Sept. 1, 1945, which has now been declassified. 



1 Shannon, C. E., "A Mathematical Theory of Communication," Bell System Technical 

 Journal, July 1948, p. 379; Oct. 1948, p. 623. 



2 See, for example, H. F. Gaines, "Elementary Cryptanalysis," or M. Givierge, "Cours 

 de Crj^tographie." 



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