Abstract
A paper by Luby and Rackoff on the construction of pseudorandom permutations from pseudorandom functions based on a design principle of the DES has recently initiated a burst of research activities on applications and generalizations of these results. This paper presents a strongly simplified treatment of these results and generalizes them by pointing out the relation to locally random functions, thereby providing new insight into the relation between probability-theoretic and complexity-theoretic results in cryptography. The first asymptotically-optimal construction of a locally random function is presented and new design strategies for block ciphers based on these results are proposed.
Chapter PDF
Similar content being viewed by others
Keywords
References
N. Alon, O. Goldreich, J. Hastad and R. Peralta, Simple constructions of almost k-wise independent random variables, Proceedings of the 31st IEEE Symposium on Foundations of Computer Science, pp. 544–553, 1990.
M. Blum and S. Micali, How to generate cryptographically strong sequences of pseudo-random bits, SIAM Journal on Computing, Vol. 10, pp. 96–113, 1981.
B. Chor and O. Goldreich, On the power of two-point based sampling, Journal of Complexity, Vol. 5, No. 1, pp. 96–106, 1989.
D.E. Denning, Cryptography and Data Security, Addison-Wesley, Reading, MA, 1983.
O. Goldreich, S. Goldwasser and S. Micali, How to construct random functions, Journal of the Association for Computing Machinery, Vol. 33, pp. 792–807, 1986.
A. Joffe, On a set of almost deterministic k-independent random variables, The Annals of Probability, Vol. 2, No. 1, pp. 161–162, 1974.
H.O. Lancaster, Pairwise statistical independence, Ann. Math. Statist., Vol. 36, pp. 1313–1317, 1965.
L.A. Levin, One-way functions and pseudorandom generators, Proc. 17th ACM Symposium on Theory of Computing, pp. 363–364, 1985.
M. Luby and C. Rackoff, How to construct pseudorandom permutations from pseudorandom functions, SIAM Journal on Computing, Vol. 17, No. 2, pp. 373–386, 1988.
U.M. Maurer and J.L. Massey, Local randomness in pseudo-random sequences, Journal of Cryptology, Vol. 4, No. 2, pp. 135–149, 1991.
J. Patarin, Etude des générateurs de permutations basés sur le Schéma du D.E.S., Ph. D. Thesis, INRIA, Domaine de Voluceau, 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.
J. Pieprzyk, How to construct pseudorandom permutations from single pseudorandom functions, Advances in Cryptology — EUROCRYPT’90, I.B. Damgård (Ed.), Lecture Notes in Computer Science, Vol. 473, Springer-Verlag, pp. 140–150, 1991.
C.P. Schnorr, On the construction of random number generators and random function generators, Advances in Cryptology — EUROCRYPT’88, C.G. Günther (Ed.), Lecture Notes in Computer Science, Vol. 330, Springer-Verlag, pp. 225–232, 1988.
Y. Zheng, T. Matsumoto and H. Imai, Impossibility and optimality results on constructing pseudorandom permutations, Advances in Cryptology — EUROCRYPT’89, J.-J. Quisquater et al. (Eds.), Lecture Notes in Computer Science, Vol. 434, Springer-Verlag, pp. 412–421, 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Maurer, U.M. (1993). A Simplified and Generalized Treatment of Luby-Rackoff Pseudorandom Permutation Generators. In: Rueppel, R.A. (eds) Advances in Cryptology — EUROCRYPT’ 92. EUROCRYPT 1992. Lecture Notes in Computer Science, vol 658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47555-9_21
Download citation
DOI: https://doi.org/10.1007/3-540-47555-9_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56413-3
Online ISBN: 978-3-540-47555-2
eBook Packages: Springer Book Archive