Abstract
An (χY)-random system takes inputs X 1 X 2,... ∈ χ and generates, for each new input X i , an output Y i ∈ Y, depending probabilistically on X 1,..., X i and Y 1,..., Y i-1. Many cryptographic systems like block ciphers, MAC-schemes, pseudo-random functions, etc., can be modeled as random systems, where in fact Y i often depends only on X i, i.e., the system is stateless. The security proof of such a system (e.g. a block cipher) amounts to showing that it is indistinguishable from a certain perfect system (e.g. a random permutation).
We propose a general framework for proving the indistinguishability of two random systems, based on the concept of the equivalence of two systems, conditioned on certain events. This abstraction demonstrates the common denominator among many security proofs in the literature, allows to unify, simplify, generalize, and in some cases strengthen them, and opens the door to proving new indistinguishability results.
We also propose the previously implicit concept of quasi-randomness and give an efficient construction of a quasi-random function which can be used as a building block in cryptographic systems based on pseudorandom functions.
Supported in part by the Swiss National Science Foundation, grant 2000-055466.98
Chapter PDF
Similar content being viewed by others
Key words
References
M. Bellare, O. Goldreich, and H. Krawczyk, Stateless evaluation of pseudorandom functions: security beyond the birthday barrier, Advances in Cryptology-CRYPTO’ 99, Lecture Notes in Computer Sc, vol. 1666, pp. 270–287, Springer-Verlag, 1999.
M. Bellare, J. Kilian, and P. Rogaway, The security of the cipher block chaining message authentication code, Advances in Cryptology-CRYPTO’ 94, Lecture Notes in Computer Science, vol. 839, pp. 341–358, Springer-Verlag, 1995.
M. Bellare, J. Guérin, and P. Rogaway, XOR MACs: New methods for message authentication using finite pseudorandom functions, Advances in Cryptology-CRYPTO’ 95, Lecture Notes in Computer Science, vol. 963, Springer-Verlag, 1994.
D. J. Bernstein, How to stretch random functions: The security of protected counter sums, Journal of Cryptology, vol. 12, pp. 185–192, Springer-Verlag, 1999.
J. Black, S. Halevi, H. Krawczyk, T. Krovetz, and P. Rogaway, UMAC: Fast and secure message authentication, Advances in Cryptology-CRYPTO’ 99, Lecture Notes in Computer Science, vol. 1666 pp. 216–233, Springer-Verlag, 1999.
R. E. Blahut, Principles and practice of information theory, Addison-Wesley Publishing Company, 1988.
M. Blum and S. Micali, How to generate cryptographically strong sequences of pseudo-random bits, SIAM J. on Computing, vol. 13, no. 4, pp. 850–864, 1984.
O. Goldreich, S. Goldwasser, and S. Micali, How to construct random functions, Journal of the ACM, vol. 33, no. 4, pp. 210–217, 1986.
M. Luby, Pseudorandomness and Cryptographic Applications, Princeton University Press, 1996.
M. Luby and C. Rackoff, How to construct pseudo-random permutations from pseudo-random functions, SIAM J. on Computing, vol. 17, no. 2, pp. 373–386, 1988.
U.M. Maurer, Conditionally-perfect secrecy and a provably-secure randomized cipher, Journal of Cryptology, vol. 5, pp. 53–66, Springer-Verlag, 1992.
-, A simplified and generalized treatment of Luby-Rackoff pseudo-random permutation generators, Advances in Cryptology-EUROCRYPT’ 92, Lecture Notes in Computer Science, vol. 658, pp. 239–255, Springer-Verlag, 1992.
-, Extended version of this paper, see http://www.crypto.ethz.ch/publications/.
J. Patarin, Etude des générateurs de permutations basés sur le Schéma du D.E.S., Ph. D. Thesis, INRIA, Le Chesnay, France, 1991. An extract appeared in: J. Patarin, New results on pseudorandom permutation generators based on the DES scheme, Advances in Cryptology-CRYPTO’91, J. Feigenbaum (ed.), Lecture Notes in Computer Science, Vol. 576, Springer-Verlag, pp. 301–312, 1992.
-, How to construct pseudorandom permutations from a single pseudorandom function, Advances in Cryptology-EUROCRYPT’ 92, R. Rueppel (ed.), Lecture Notes in Computer Science, vol. 658, pp. 256–266, Springer-Verlag, 1992.
-, About Feistel schemes with six (or more) rounds, Fast Software Encryption, Lecture Notes in Computer Science, vol. 1372, pp. 103–121, Springer-Verlag, 1998.
E. Petrank and C. Rackoff, CBC MAC for real-time data sources, Journal of Cryptology, vol. 13, no. 3, pp. 315–338, 2000.
M. Naor and O. Reingold, On the construction of pseudorandom permutations: Luby-Rackoff revisited, Journal of Cryptology, vol. 12, no. 1, pp. 29–66, 1999.
M. O. Rabin, Transaction protection by beacons, J. Comp. Sys. Sci., vol. 27, pp. 256–267, 1983.
V. Shoup, On fast and provably secure message authentication based on universal hashing, Advances in Cryptology-CRYPTO’ 96, Lecture Notes in Computer Science, vol. 1109, pp. 313–328, Springer-Verlag, 1996.
S. Vaudenay, Provable security for block ciphers by decorrelation, Proceedings of STACS’98, Lecture Notes in Computer Science, vol. 1373, Springer-Verlag, pp. 249–275, 1998.
-, On provable security for conventional ciphers, in Proc. of ICISC’99, Lecture Notes in Computer Science, Springer-Verlag, 1999.
M. N. Wegman and J. L. Carter, New hash functions and their use in authentication and set equality, J. of Computer and System Sciences, vol. 22, pp. 265–279, 1981.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maurer, U. (2002). Indistinguishability of Random Systems. In: Knudsen, L.R. (eds) Advances in Cryptology — EUROCRYPT 2002. EUROCRYPT 2002. Lecture Notes in Computer Science, vol 2332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46035-7_8
Download citation
DOI: https://doi.org/10.1007/3-540-46035-7_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43553-2
Online ISBN: 978-3-540-46035-0
eBook Packages: Springer Book Archive