Random ciphering bounds on a class of secrecy systems and discrete message sources

The problem of enciphering a stationary finite discrete message so that a cryptanalyst is unlikely to decrypt an intercepted cryptogram is considered. Additive-like instantaneous block (ALIB) encipherers are studied that employ a list of
e^{nr}
keywords of length
n
, called the cipher. An ALIB encipherer produces a cryptogram word of length
n
from a message word and a key word of the same length by combining corresponding message letters and key-word letters. Certain technical restrictions sure placed on the combining function. The decipherer uses a decoder which combines a letter from the key word used in enciphering with a letter from the cryptogram to form a letter of the decoded message. cryptanalyst also decodes letter by letter with an identical decoder; however, he uses a keyword that is not necessarily that used in enciphering. For a given message source and combiner, the design of the cipher consists in choosing the block length
n
, the key rate
r
, and the set of
e^{nr}
key words. These are to be chosen so that
p_{w}
, the probability of correct decryptment of the message word, and
p( \Delta)
, the probability that the per letter nonzero Hamming distance between the decrypted message and the true message is smaller than
\Delta
, are very small for every cryptanalyst. A set of pairs
( \Delta,r)
for which there exist ciphers with key rate
r
such that,
p_{w}
and
p( \Delta)
can be made arbitrarily small for every cryptanalyst is determined using the concepts of random ciphering and exponential bounding.