Communication Theory of Secrecy Systems - Network Research Lab

A running key cipher is a Vernam type system where, in place of a random
sequence of letters, the key is a meaningful text. Now it is known that running
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 increase 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 solved without the key. If one uses in place of one
English text, about d 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 messages as possible without
running the risk of multiple reconstructions, and then encipher the residue.
Since 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 approaching
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 founded by giving the
distribution of equivocation. For N intercepted letters we consider the fraction
of cryptograms for which the equivocation (for these particular E’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 +
dH. 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 HE(M), N 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 HE(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.
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