Volume 8, no. 1Pages 111 - 127 Some Generalizations of Shannon's Theory of Perfect Ciphers
S.M. RatseevK. 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. Also in this cipher should be used equiprobable key sequences that are not always reached. In this review paper discusses the problems of constructing perfect and (k|y)-perfect ciphers for a given set of parameters. We give necessary and sufficient conditions for these ciphers. We construct perfect and (k|y)-perfect substitution ciphers with unlimited key and imitation resistant perfect ciphers. We study the case when the random generator of key sequences does not necessarily have a uniform probability distribution.
Full text- Keywords
- cipher; perfect cipher; imitation of message.
- References
- 1. Alferov A.P., Zubov A.Yu., Kuz'min A.S., Cheremushkin A.V. Osnovy kriptografii [Foundations of Cryptography]. Moscow, Gelios ARV, 2005. 480 p.
2. Zubov A.Yu. Kriptograficheskie metody zashhity informacii. Sovershennye shifry [Cryptographic Methods of Information Security. Perfect ciphers]. Moscow, Gelios ARV, 2005. 192 p.
3. Ratseev S.M., Cherevatenko O.I. [On Perfect Ciphers Based on Orthogonal Tables]. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming & Computer Software, 2014, vol. 7, issue 2, pp. 66-73. (in Russian)
4. Ratseev S.M. [On Perfect Imitation Resistant Ciphers]. Prikladnaya Diskretnaya Matematika [Applied Discrete Mathematics], 2012, vol. 17, issue 3, pp. 41-47. (in Russian)
5. Ratseev S.M. [On Perfect Imitation Resistant Ciphers with Unbounded Key]. Vestnik Samarskogo Gosudarstvennogo Universiteta [ Vestnik Samara Proposition University], 2013, vol. 110, issue 9/1, pp. 45-50. (in Russian)
6. Ratseev S.M. [On Construction of Perfect Ciphers]. Vestn. Samar. Gos. Tekhn. Univ. Ser. Fiz.-Mat. Nauki [Journal of Samara State Technical University. Ser. Physical and Mathematical Sciences], 2014, vol. 34, issue 1, pp. 192-199. (in Russian)
7. Ratseev S.M. [On Theoretically Perfect Ciphers ]. Sistemy i sredstva informatiki [ Systems and Means of Informatics], 2014, vol. 24, issue 1, pp. 61-72. (in Russian)
8. Holl M. Combinatorics. Waltham (Massachusetts), Blaisdell Publishing, 1967. 310 p.