On theoretically perfect ciphers

K. Shannon in the 1940s introduced the concept of a perfect cipher, which provides the best protection of plaintexts. Perfect secrecy means that a cryptanalyst can obtain no information about the plaintext by observing the ciphertext. It is well known that the Vernam cipher with equiprobable gamma is a perfect cipher but it is not imitation resistant because it uses equipotent alphabets for plaintexts and ciphertexts. On the basis of A. Yu. Zubov's mathematical model of the substitution cipher with the unbounded key, the models of perfect and imitation resistant ciphers were constructed. In this case, the bearing cipher of the model is perfect and reaches the lower bounds for the probability of success of imitation and substitution of ciphertexts. The paper also gives some generalizations of the classical theory of K. Shannon on perfect ciphers.