Volume 7, no. 2Pages 66 - 73

On Perfect Ciphers Based on Orthogonal Tables

S.M. Ratseev, O.I. Cherevatenko
We study perfect imitation resistant ciphers, highlighting particularly the case in which the probabilities of successful imitation and substitution attain their lower limits. It is known that the Vernam cipher with equiprobable gamma is a perfect cipher, but it is maximally vulnerable to imitation attempts owing to its use of alphabets of the same size for plaintexts and ciphertexts. Since the limitation on the size of the sets of plaintexts and keys is a drawback of the mathematical model of the cipher, we begin by studying Zubov's mathematical model of substitution cipher with unbounded key. Basing on this model, we construct models of perfect imitation resistant ciphers. These ciphers use orthogonal tables and Latin rectangles. We study the case in which the generator of random key sequences need not have the uniform probability distribution. Since the keys of these ciphers are at least as long as the transmitted messages, substitution ciphers with unbounded key should be used in very important cases.
Full text
cipher; perfect cipher; imitation of message.
1. Holl M. Combinatorics. Waltham (Massachusetts), Blaisdell Publishing, 1967. 310 p.
2. Bose R.S. On the Applications of the Properties of Galois Fields to the Problems of Construction of Hyper-Graeco-Latin Square. Indian J. Stat, 1938, vol. 4, issue 3, pp. 323-338.
3. Zubov A.Yu. Kriptograficheskie metody zashhity informacii. Sovershennye shifry [Cryptographic Methods of Information Security. Perfect Ciphers]. Moscow, Gelios ARV, 2005. 192 p.
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. Estestvennonauchnaya seriya [Vestnik of Samara State University. Natural Science Series], 2013, vol. 110, issue 9/1, pp. 45-50. (in Russian)
6. Ratseev S.M. [On optimal Authentication Code]. Sistemy i Sredstva Informatiki [ Systems and Means of Informatics], 2013, vol. 23, issue 1, pp. 53-57. (in Russian)