Abstract
Knapsack-based cryptosystems used to be popular in the beginning of public key cryptography before being all broken, all but the Chor-Rivest cryptosystem. In this paper, we show how to break this one with its suggested parameters: GF(p 24) and GF(25625). We also give direction on possible extensions of our attack.
Part of this work was done when the author was visiting AT&T Labs Research.
Chapter PDF
References
P. Camion, H. Chabanne. On the Powerline system. In Advances in Cryptology, ICICS'97, Beijing, China, Lectures Notes in Computer Science 1334, pp. 381–385, Springer-Verlag, 1997.
B. Chor, R.L. Rivest. A knapsack-type public key cryptosystem based on arithmetic in finite fields. In Advances in Cryptology CRYPTO'84, Santa Barbara, California, U.S.A., Lectures Notes in Computer Science, pp. 54–65, Springer-Verlag, 1985.
B. Chor, R.L. Rivest. A knapsack-type public key cryptosystem based on arithmetic in finite fields. IEEE Transactions on Information Theory, vol. IT-34, pp. 901–909, 1988.
D. Coppersmith, J. Stern, S. Vaudenay. The security of the birational permutation signature schemes. Journal of Cryptology, vol. 10, pp. 207–221, 1997.
K. Huber. Specialised attack on Chor-Rivest public key cryptosystem. Electronics Letters, vol. 27, no. 23, pp. 2130, 1991.
A. Joux, J. Stern. Lattice Reduction: a Toolbox for the Cryptanalyst. To appear in Journal of Cryptology.
N. Koblitz. A Course in Number Theory and Cryptography, 2nd Edition, Graduate Texts in Mathematics 114, Springer-Verlag, 1994.
H.W. Lenstra, Jr. On the Chor-Rivest Knapsack Cryptosystem. Journal of Cryptology, vol. 3, pp. 149–155, 1991.
A.K. Lenstra, H.W. Lenstra Jr., L. Lovász. Factoring polynomials with rational coefficients. Math. Ann., vol. 261, pp. 515–534, 1982.
R.C. Merkle, M. Hellman. Hiding information and signatures in trap-door knap-sacks. IEEE Transactions on Information Theory, vol. IT-24, pp. 525–530, 1978.
S. Pohlig, M. Hellman. An improved algorithm for computing logarithms over GF(q) and its cryptographic significance. IEEE Transactions on Information Theory, vol. IT-24, pp. 106–110, 1978.
A. Shamir. A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem. In Proceedings of the 23rd IEEE Symposium on Foundations of Computer Science, Chicago, Illinois, U.S.A., pp. 145–152, IEEE, 1982.
C.P. Schnorr, H.H. Hörner. Attacking the Chor-Rivest Cryptosystem by improved lattice reduction. In Advances in Cryptology EUROCRYPT'95, Saint-Malo, France, Lectures Notes in Computer Science 921, pp. 1–12, Springer-Verlag, 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vaudenay, S. (1998). Cryptanalysis of the Chor-Rivest cryptosystem. In: Krawczyk, H. (eds) Advances in Cryptology — CRYPTO '98. CRYPTO 1998. Lecture Notes in Computer Science, vol 1462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055732
Download citation
DOI: https://doi.org/10.1007/BFb0055732
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-64892-5
Online ISBN: 978-3-540-68462-6
eBook Packages: Springer Book Archive