Communication Theory of Secrecy Systems - Network Research Lab

is that the decipherer knows the particular key being used, while the cryptanalyst
knows only the a priori probabilities of the various keys in the set.
The process of deciphering is that of applying the inverse of the particular
transformation used in enciphering to the cryptogram. The process of cryptanalysis
is that of attempting to determine the message (or the particular key)
given only the cryptogram and the a priori probabilities of various keys and
messages.
There are a number of difficult epistemological questions connected with
the theory of secrecy, or in fact with any theory which involves questions
of probability (particularly a priori probabilities, Bayes’ theorem, etc.) when
applied to a physical situation. Treated abstractly, probability theory can be
put on a rigorous logical basis with the modern measure theory approach 45 .
As applied to a physical situation, however, especially when “subjective”
probabilities and unrepeatable experiments are concerned, there are many
questions of logical validity. For example, in the approach to secrecy made
here, a priori probabilities of various keys and messages are assumed known
by the enemy cryptographer—how can one determine operationally if his estimates
are correct, on the basis of his knowledge of the situation?
One can construct artificial cryptographic situations of the “urn and die”
type in which the a priori probabilities have a definite unambiguous meaning
and the idealization used here is certainly appropriate. In other situations that
one can imagine, for example an intercepted communication between Martian
invaders, the a priori probabilities would probably be so uncertain as to
be devoid of significance. Most practical cryptographic situations lie somewhere
between these limits. A cryptanalyst might be willing to classify the
possible messages into the categories “reasonable”, “possible but unlikely”
and “unreasonable”, but feel that finer subdivision was meaningless.
Fortunately, in practical situations, only extreme errors in a priori probabilities
of keys and messages cause significant errors in the important parameters.
This is because of the exponential behavior of the number of messages
and cryptograms, and the logarithmic measures employed.
3 REPRESENTATION OF SYSTEMS
A secrecy system as defined above can be represented in various ways. One
which is convenient for illustrative purposes is a line diagram, as in Figs. 2
and 4. The possible messages are represented by points at the left and the
possible cryptograms by points at the right. If a certain key, say key 1, transforms
message M2 into cryptogram E4 then M2 and E4 are connected by a
4 See J. L. Doob, “Probability as Measure”, Annals of Math. Stat., v. 12, 1941, pp. 206–214.
5 A. Kolmogoroff, “Grundbegriffe der Wahrscheinlichkeitsrechnung”, Ergebnisse der Mathematic, v.
2, No. 3 (Berlin 1933).
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