Abstract
At SAC’ 97, Itoh, Okamoto and Mambo presented a fast public key cryptosystem. After analyzing several attacks including latticereduction attacks, they claimed that its security was high, although the cryptosystem had some resemblances with the former knapsack cryptosystems, since decryption could be viewed as a multiplicative knapsack problem. In this paper, we show how to recover the private key from a fraction of the public key in less than 10 minutes for the suggested choice of parameters. The attack is based on a systematic use of the notion of the orthogonal lattice which we introduced as a cryptographic tool at Crypto ’97. This notion allows us to attack the linearity hidden in the scheme.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
K. Itoh, E. Okamoto, and M. Mambo. Proposal of a fast public key cryptosystem. In Proc. of Selected Areas in Cryptography’ 97, 1997. Available at http://adonis.ee.queensu.ca:8000/sac/sac97/papers/paper10.ps.
A. K. Lenstra, H. W. Lenstra, and L. Lovász. Factoring polynomials with rational coefficients. Math. Ann., 261:515–534, 1982.
R. Merkle and M. Hellman. Hiding information and signatures in trapdoor knapsacks. IEEE Trans. Inform. Theory, IT-24:525–530, September 1978.
D. Naccache and J. Stern. A new public-key cryptosystem. In Proc. of Eurocrypt’ 97, volume 1233 of LNCS, pages 27–36. Springer-Verlag, 1997.
P. Nguyen and J. Stern. Merkle-Hellman revisited: a cryptanalysis of the Qu-Vanstone cryptosystem based on group factorizations. In Proc. of Crypto’ 97, volume 1294 of LNCS, pages 198–212. Springer-Verlag, 1997.
P. Nguyen and J. Stern. The Béguin-Quisquater server-aided RSA protocol from Crypto’ 95 is not secure. In Proc. of Asiacrypt’ 98, LNCS. Springer-Verlag, 1998.
P. Nguyen and J. Stern. Cryptanalysis of the Ajtai-Dwork cryptosystem. In Proc. of Crypto’ 98, volume 1462 of LNCS, pages 223–242. Springer-Verlag, 1998.
A. Odlyzko. Cryptanalytic attacks on the multiplicative knapsack cryptosystem and on Shamir’s fast signature scheme. IEEE Trans. Inform. Theory, IT-30:594–601, 1984.
V. Shoup. Number Theory C++ Library (NTL) version 2.0. Can be obtained at http://www.cs.wisc.edu/~shoup/ntl/.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Nguyen, P., Stern, J. (1999). Cryptanalysis of a Fast Public Key Cryptosystem Presented at SAC ’97. In: Tavares, S., Meijer, H. (eds) Selected Areas in Cryptography. SAC 1998. Lecture Notes in Computer Science, vol 1556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48892-8_17
Download citation
DOI: https://doi.org/10.1007/3-540-48892-8_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65894-8
Online ISBN: 978-3-540-48892-7
eBook Packages: Springer Book Archive