Communication Theory of Secrecy Systems - Network Research Lab

simple substitution will be approximately as show in Fig. 10. The Vigenère,
Playfair and Fractional cases are more likely to follow the theoretical formulas
for random ciphers than simple substitution and transposition. The reason
for this is that they are more complex and give better mixing characteristics
to the messages on which they operate.
The mixed alphabet Vigenère (each of d alphabets mixed independently
and used sequentially) has a key size,
H(K) = d log 26! = 26.3d
and its unicity point should be at about 53d letters.
These conclusions can also be put to a rough experimental test with the
Caesar type cipher. In the particular cryptogram analyzed in Table 1, section
11, the function HE(K, N) has been calculated and is given below, together
with the values for a random cipher.
N 0 1 2 3 4 5
H(observed) 1.41 1.24 .97 .60 .28 0
H(calculated) 1.41 1.25 .98 .54 .15 .03
The agreement is seen to be quite good, especially when we remember
that the observed H should actually be the average of many different cryptograms,
and that H for the larger values of N is only roughly estimated.
It appears then that the random cipher analysis can be used to estimate
equivocation characteristics and the unicity distance for the ordinary types of
ciphers.
16 VALIDITY OF A CRYPTOGRAM SOLUTION
The equivocation formulas are relevant to questions which sometimes arise
in cryptographic work regarding the validity of an alleged solution to a cryptogram.
In the history of cryptography there have been many cryptograms,
or possible cryptograms, where clever analysts have found a “solution”. It
involved, however, such a complex process, or the material was so meager
that the question arose as to whether the cryptanalyst had “read a solution”
into the cryptogram. See, for example, the Bacon-Shakespeare ciphers and
the “Roger Bacon” manuscript. 11
In general we may say that if a proposed system and key solves a cryptogram
for a length of material considerably greater than the unicity distance
the solution is trustworthy. If the material is of the same order of shorter than
the unicity distance the solution is highly suspicious.
This effect of redundancy in gradually producing a unique solution to a
cipher can be thought of in another way which is helpful. The redundancy is
essentially a series of conditions on the letters of the message, which insure
11 See Fletcher Pratt, loc. cit.
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