Browse > Article
http://dx.doi.org/10.13089/JKIISC.2004.14.1.47

Chosen Message Attack Against Goldreich-Goldwasser-Halevi's Lattice Based Signature Scheme  

DaeHun Nyang (Inha Univ.)
Publication Information
Journal of the Korea Institute of Information Security & Cryptology / v.14, no.1, 2004 , pp. 47-57 More about this Journal
Abstract
The Goldreich-Goldwasser-Halevi(GGH)'s signature scheme from Crypto '97 is cryptanalyzed, which is based on the well-blown lattice problem. We mount a chosen message attack on the signature scheme, and show the signature scheme is vulnerable to the attack. We collects n lattice points that are linearly independent each other, and constructs a new basis that generates a sub-lattice of the original lattice. The sub-lattice is shown to be sufficient to generate a valid signature. Empirical results are presented to show the effectiveness of the attack Finally, we show that the cube-like parameter used for the private-key generation is harmful to the security of the scheme.
Keywords
Public-key cryptography; Lattice; Closest Vector Problem; GGH's Cryptosystem; Chosen message attack;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Ajtai, Generating hard instances of lattice problems, In Proceedings of 28th STOC, Philadelphia, 1996. pp. 99-108
2 P. Van Emde Boas. Another NP-complete problem and the complexity of computing short vectors in a lattice Report 81-04, Mathematische Institut University of Amsterdam, 1981
3 M. Ajtai, and C. Dwork, A public-key cryptosystem with worst-case/average-case equivalence, In Proceedings of 29th STOC. Texas, 1997, pp. 284-293
4 P. Nguyen, Cryptanalysis of the Gold reich-Goldwasser-Halevi Cryptosystem from Crypto '97, In Proceedings of CRYPT0'99, Santa Barbara, CA, 1999, pp. 112-131
5 L. Babai, On Lovasz lattice reduction and the nearest lattice point problem. Combinatorica. Vol.6, No.1, 1986, pp. 113
6 O. Goldreich, S. Goldwasser, and S. Halvei, , In Proceedings of CRYPT0'97, Santa Barbara CA, 1997, pp. 112-131Public-key cryptosystems from lattice reduction problems
7 A. K. Lenstra, H. W. Lenstra, L. Lovasz, Factoring polynomials with rational coefficients. Mathematische Annalen 261, 1982, pp. 515-534
8 LiDIA, A C++ Library For Computational Number Theory, Available from http://www.informatik.th-darmstadt.de/TI/LiDIA/Welcome.html