Abstract
The paper shows that an “informal” interpretation of one-way functions in modern cryptography is inadequate and defines such functions in terms of information theory. This combination of complexity and information theories opens new opportunities for constructing one-way functions, whose one-way transformation is based on the ambiguity of their inverse mappings. It is shown that random mappings are promising candidates for constructing such functions.
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References
W. Diffie and M. E. Hellman, “New directions in cryptography,” IEEE Trans. Inform. Theory, 22, 644–654 (1976).
R. L. Rivest, A. Shamir, and L. M. Adleman, “A method for obtaining digital signatures and public key cryptosystem,” ACM Commun., 21, No. 2, 120–126 (1978).
“Digital signature standard (DSS),” in: FIPS PUB 186-1:1998, USA, Washington, DC, U.S. Dep. of Commerce. Nat. Bureau of Standards, Dec. (1998).
T. ElGamal, “A public-key cryptosystem and a signature scheme based on discrete logarithms,” IEEE Trans. Inform. Theory, 31, 469–472 (1985).
C. P. Schnorr, “Efficient identification and a signature for smart card,” J. Cryptology, Lect. Notes Comput. Sci., 435, 239–252 (1990).
N. Koblitz, “Elliptic curve cryptography,” Math. Comput., 48, 203–209 (1987).
N. I. Ptitsyn, Application of the Theory of Deterministic Chaos to Cryptography [in Russian], MGTU, Moscow (2002).
L. Kocarev, “Chaos-based cryptography: a brief overview,” IEEE Circuits and Systems Magazine, 1, 6–21 (2001).
L. Kocarev and Z. Tasev, “Public-key encryption based on Chebyshev maps,” Proc. IEEE Symp. on Circuits and Systems (ISCAS 2003), 3 (2003), pp. 28–31.
N. Masuda and K. Aihara, “Cryptosystem with discretized chaotic maps,” IEEE Trans. on Circuits and Systems, 1: Fundamental Theory and Applications, 49, No. 1, 28–39 (2002).
Z. Kotulski, J. Szczepanski, K. Gorski, et al., “Application of discrete chaotic dynamical systems in cryptography — DCC method,” Intern. J. Bifurc. Chaos, 9, 1121–1135 (1999).
S. Goldwasser and M. Bellare, “Lecture notes on cryptography,” J. Computer and System Sci., 28, No. 2, 270–299 (1984).
K. Shannon, “A mathematical theory of communication,” in: Papers in Information Theory and Cybernetics [Russian translation], Izd. Inostr. Lit., Moscow (1963), pp. 243–332.
K. Shannon, “Communication theory of secrecy systems,” in: Papers in Information Theory and Cybernetics [Russian translation], Izd. Inostr. Lit., Moscow (1963), pp. 333–369.
H. G. Schuster, Deterministic Chaos, Physik-Verlag, Weinheim (1984).
I. M. Vinogradov, Fundamentals of the Number Theory [in Russian], Nauka, Moscow (1972).
T. Kohda, “Information sources using chaotic dynamics,” Proc. IEEE, 90, No. 5, 641–661 (2002).
A. S. Dmitriev and S. O. Starkov, “Messaging based on chaos and classical information theory,” Zarubezhn. Radioelektr., Uspekhi Sovr. Radioelektr., No. 11, 4–32 (1998).
P. Yu. Kostenko, S. I. Sivashchenko, A. V. Antonov, and T. P. Kostenko, “Application of the methods of chaotic dynamics to provide information security in communication systems and networks,” Izv. VUZov, Radioelektronika, 49, No. 3, 63–70 (2006).
P. Yu. Kostenko, A. V. Antonov, and T. P. Kostenko, “Analysis of uniqueness of the solution of inverse problems of chaotic dynamics to provide information security in communication systems and networks,” Izv. VUZov, Radioelektronika, 49, No. 8, 3–11 (2006).
Z. Kotulski, J. Szczepanski, K. Gorski, et al., “On constructive approach to chaotic pseudorandom number generators,” in: Proc. Region. Conf. on Milit. Commun. Inform. Syst., CIS Solutions for an Enlarged NATO (RCMCIS’2000) (2000), pp. 191–203.
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Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 136–146, November–December 2006.
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Kostenko, P.Y., Antonov, A.V. & Kostenko, T.P. Developing the concept of one-way functions for cryptographic security systems using achievements in chaotic dynamics. Cybern Syst Anal 42, 884–891 (2006). https://doi.org/10.1007/s10559-006-0128-x
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DOI: https://doi.org/10.1007/s10559-006-0128-x