Systems and Means of Informatics
2014, Volume 24, Issue 1, pp 61-72
ON THEORETICALLY PERFECT CIPHERS
Abstract
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 Vernamcipherwith 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.
[+] References (7)
- Alferov, A.P., A.Yu. Zubov, A. S. Kuz'min, and A.V. Cheremushkin. 2005. Osnovy
kriptografii [Foundations of cryptography].Moscow: Gelios ARV. 480 p.
- Ratseev, S.M. 2012. O sovershennykh imitostoykikh shifrakh [On perfect imitation
resistant ciphers].Prikladnaya DiskretnayaMatematika [Applied Discrete Mathematics]
17(3):41-47.
- Ratseev, S.M. 2013. O sovershennykh imitostoykikh shifrakh zameny s neogranichennym klyuchom [On perfect imitation resistant ciphers with unbounded key]. Vestnik Samarskogo Gosudarstvennogo Universiteta [Vestnik Samara State University]
110(9/1):42-48.
- Zubov, A.Yu. 2005. Kriptograficheskie metody zashchity informatsii. Sovershennye
shifry [Cryptographic methods of information security. Perfect ciphers]. Moscow: Gelios
ARV. 192 p.
- Ratseev, S.M. 2013.Ob optimal'nykh kodakh autentifikatsii [On optimal authentication
code]. Sistemy i Sredstva Informatiki|Systems andMeans of Informatics 23(1):53-57.
- Holl, M. 1967. Combinatorics.Waltham, MA: Blaisdell Publ., 1967. 310 p.
- Tuzhilin, M. E. 2012. Latinskie kvadraty i ikh primenenie v kriptografii [Latin squares
and their applications in cryptography]. Prikladnaya Diskretnaya Matematika [Applied
Discrete Mathematics] 17(3):47-52.
[+] About this article
Title
ON THEORETICALLY PERFECT CIPHERS
Journal
Systems and Means of Informatics
Volume 24, Issue 1, pp 61-72
Cover Date
2013-11-30
DOI
10.14357/08696527140103
Print ISSN
0869-6527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
cipher; perfect cipher; imitation resistant ciphers
Authors
S.M. Ratseev 
Author Affiliations
Department of Information Security and Control Theory, Faculty of Mathematics and Information Technologies, Ulyanovsk State University, 42 Lev Tolstoy Str.,
Ulyanovsk 432017, Russian Federation
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