Communication Theory of Secrecy Systems - Network Research Lab

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stitution cipher applied to English, this calculation gave the curves shown in Fig. 9. The key appearance characteristic in this case was estimated by counting the number of different letters appearing in typical English passages of N letters. In so far as experimental data on simple substitution could be found, they agree very well with the curves of Fig. 9, considering the various idealizations and approximations which have been made. For example, the unicity point, at about 27 letters, can be shown experimentally to lie between the Fig. 8. Graphical calculation of equivocation limits 20 and 30. With 30 letters there is nearly always a unique solution to a cryptogram of this type and with 20 it is usually easy to find a number of solutions. With transposition of period d (random key), H(K) = log d!, or about d log d (using a Stirling approximation for d!). If we take .6 decimal digits per e letter as the appropriate redundancy, remembering the preservation of letter frequencies, we obtain about 1.7d log d e as the unicity distance. This also checks fairly well experimentally. Note that in this case HE(M) is defined only for integral multiples of d. With the Vigenère the unicity point will occur at about 2d letters, and this too is about right. The Vigenère characteristic with the same key size as 695
Fig. 9. Equivocation for simple substitution on English 696
Page 1 and 2: Communication Theory of Secrecy Sys
Page 3 and 4: the cryptanalyst being assumed to h
Page 5 and 6: index—theoretical in that it allo
Page 7 and 8: At the receiving end it must be pos
Page 9 and 10: is that the decipherer knows the pa
Page 11 and 12: 4.2 Transposition (Fixed Period d)
Page 13 and 14: The matrix aij is the key, and deci
Page 15 and 16: 5.2 Size of Key The key must be tra
Page 17 and 18: It may be noted that multiplication
Page 19 and 20: the same as the M space, i.e., that
Page 21 and 22: (4) Each message in Ci can be encip
Page 23 and 24: The columns are then cut apart and
Page 25 and 26: of the values of these. In this cas
Page 27 and 28: In a secrecy system there are two s
Page 29 and 30: text has been started at a random p
Page 31 and 32: in which E, M and K are the cryptog
Page 33 and 34: If we have a product system S = T R
Page 35 and 36: 13 EQUIVOCATION FOR SIMPLE SUBSTITU
Page 37 and 38: keys from high probability messages
Page 39: 1. We assumed for the random cipher
Page 43 and 44: simple substitution will be approxi
Page 45 and 46: Theorem 12. A necessary and suffici
Page 47 and 48: On the other hand, if the language
Page 49 and 50: much higher) work characteristic. A
Page 51 and 52: the number of trials) only 88 trial
Page 53 and 54: serves to limit the possible keys t
Page 55 and 56: and all the fi involve all the ki.
Page 57 and 58: egion F R is equal to the measure o
Page 59 and 60: 27 INCOMPATIBILITY OF THE CRITERIA

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