COMMUNICATION THEORY OF SECRECY SYSTEMS 701 



A running key ciplier is a Vernani type system where, in place of a random 

 sequence of letters, the key is a meaningful text. Now it is known that run- 

 ning key ciphers can usually be solved uniquely. This shows that English 

 can be reduced by a factor of two to one and implies a redundancy of at 

 least 50%. This figure cannot be increased very much, however, for a number 

 of reasons, unless long range "meaning" structure of English is considered. 



The running key cipher can be easily improved to lead to ciphering systems 

 which could not be soK^ed without the key. If one uses in place of one English 

 text, about 4 different texts as key, adding them all to the message, a 

 sufficient amount of key has been introduced to produce a high positive 

 equivocation. Another method would be to use, say, every 10th letter of 

 the text as key. The intermediate letters are omitted and cannot be used 

 at any other point of the message. This has much the same effect, since 

 these spaced letters are nearly independent. 



The fact that the vowels in a passage can be omitted without essential 

 loss suggests a simple way of greatly improving almost any ciphering system. 

 First delete all vowels, or as much of the message as possible without run- 

 ning the risk of multiple reconstructions, and then encipher the residue. 

 Since this reduces the redundancy by a factor of perhaps 3 or 4 to 1, the 

 unicity point will be moved out by this factor. This is one way of approach- 

 ing ideal systems — using the decipherer's knowledge of English as part of 

 the deciphering system. 



20. Distribution of Equivocation 



A more complete description of a secrecy system applied to a language 

 than is afforded by the equivocation characteristics can be found by giving 

 the dislribulion of equivocation. For N intercepted letters we consider the 

 fraction of cryptograms for which the equivocation (for these particular 

 £'s, not the mean He{M)) lies between certain limits. This gives a density 

 distribution function 



P(He(M), N) dHE(M) 



for the probability that for N letters H lies between the limits H and H -{- 

 (III. The mean equivocation we have previously studied is the mean of this 

 distribution. The function P{He(M), N) can be thought of as plotted along 

 a third dimension, normal to the paper, on the IIe(M), X plane. If the 

 language is pure, with a small influence range, and the cipher is pure, the 

 function will usually be a ridge in this plane whose highest point follows 

 approximately the mean IIe(M), at least until near the unicity point. In 

 this case, or when the conditions are nearly verified, the mean curve gives 

 a reasonably complete picture of the system. 



