COMMUNICATION TUEORY OF SECRECY SYSTEMS 



005 



by a line labeled 1, etc. From each possible message there must be exactly 

 one line emerging for each different key. If tlie same is true for each 

 cryptogram, we will say that the system is dosed. 



A more common way of describing a system is by stating tlie operation 

 one performs on the message for an arbitrary key to obtain the cryptogram. 

 Similarly, one detines implicitly the probabilities for various keys by de- 

 scribing how a key is chosen or what we know of the enemy's habits of key 

 choice. The {probabilities for messages are implicitly determined by stating 

 our a priori knowledge of the enemy's language habits, the tactical situation 

 (which will influence the probable content of the message) and any special 

 information we may have regarding the cryptogram. 



CLOSED SYSTEM NOT CLOSED 



Fig. 2 — Line drawings for simple systems. 



4. Some Examples of Secrecy Systems 



In this section a number of examples of ciphers will be given. These will 

 often be referred to in the remainder of the paper for illustrative purposes. 



1. Simple Substitution Cipher. 



In this cipher each letter of the message is replaced by a fixed substitute, 

 usually also a letter. Thus the message, 



M = minhmsnii- • • 



where nii , nh , • • • are the successive letters becomes: 



E = 61^263^4 • • • 



= f{nii)J{nh)f{mz)f{mi) ■ ■ ■ 



where the function /(w) is a function with an inverse. The key is a permuta- 

 tion of the alphabet (when the substitutes are letters) e.g. A' G U A C D 

 T B F H R S L M QV Y Z W I E J O K N P. The first letter A is the 

 substitute for .1 , G is the substitute for B, etc. 



