CUMMLMLATIO.\ THEORY OF SECRFXV SYSt'EMS 



703 



Although it is always possible in principle to determine these solutions 

 (by trial of each possible key for example), difTerent enciphering systems 

 show a wide variation in the amount of work required. The average amount 

 of work to determine the key for a cryptograni of X letters, W{N), measured 

 say in man hours, may be called the work characteristic of the system. This 

 average is taken over all messages and all keys with their appropriate prob- 

 abilities. The function Tr(A') is a measure of the amount of "practical 

 secrecy" afiforded by the system. 



For a simple substitution on English the work and equivocation char- 

 acteristics would be somewhat as shown in Fig. 12. The dotted portion of 



Fig. 12 — Tyjiical work and equivocation characteristics. 



the curve is in the range where there are numerous possible solutions and 

 these must all be determined. In the solid portion after the unicity point 

 only one solution exists in general, but if only the minimum necessary data 

 are given a great deal of work must be done to isolate it. As more material 

 is available the work rapidly decreases toward some asymptotic value — 

 where the additional data no longer reduces the labor. 



Essentially the behavior shown in Fig. 12 can be expected with any type 

 of secrecy system where the equivocation approaches zero. The scale of 

 man hours required, however, will differ greatly with different types of 

 ciphers, even when the He{M) curves are about the same. A Vigenere or 

 compound Vigenere, for e.xample, with the same key size would have a 



