A new perturbation algorithm and enhancing security of SFLASH signature scheme
Research Papers
First Online:
Received:
Accepted:
- 44 Downloads
- 4 Citations
Abstract
This paper introduces the concept of noise factor and noise operation, and constructs a noise group. We present a new perturbation algorithm for enhancing security of multivariate public key cryptosystems (MPKCs). European Consortium SFLASH which derives from Matsumoto-Imai scheme is a fast signature scheme intended for low cost smart cards. It was broken with the differential cryptanalysis by Dubois et al. in 2007. Taking Matsumoto-Imai system as an example, security analysis shows that the new algorithm can powerfully demolish its potential mathematical properties of the public key, and effectively avoid differential cryptanalysis without lowering the efficiency of the original algorithm.
Keywords
SFLASH differential cryptanalysis noise factor noise operation noise groupPreview
Unable to display preview. Download preview PDF.
References
- 1.Shor P W. Algorithms for quantum computation: Discrete log and factoring. In: Proceedings of the 35th Symposium on Foundations of Computer Science, New York: IEEE Computer Society Press, 1994. 124–134CrossRefGoogle Scholar
- 2.Hoffstein J, Pipher J, Silverman J H. NTRU: a ring based public key cryptosystem. In: Proc. of ANTS III, LNCS 1423. Berlin: Springer-Verlag, 1998. 267–288Google Scholar
- 3.Okamoto T, Tanaka K, Uchiyama S. Quantum public-key cryptosystems. In: CRYPTO2000, LNCS 1880. Berlin: Springer-Verlag, 2000. 147–165Google Scholar
- 4.Ding J. Multivariate Public Key Cryptosystems. Berlin: Springer-Verlag, 2006. 11–190MATHGoogle Scholar
- 5.Garey M, Johnson D. Computers and Intractability, A Guide to the Theory of NP-Completeness. New York: Freeman, 1979MATHGoogle Scholar
- 6.Patarin J, Courtois N, Goubin L. FLASH, a fast multivariate signature algorithm. In: CT-RSA 2001, LNCS 2020, Berlin: Springer-Verlag, 2001. 297–307Google Scholar
- 7.Akkar M, Courtois N, Duteuil R, et al. A fast and secure implementation of SFLASH. In: PKC2003, LNCS, Vol. 2567. Berlin: Springer, 2003. 267–278Google Scholar
- 8.Dubois V, Fouque P A, Shamir A, et al. Practical cryptanalysis of SFLASH. In: Crypto2007, LNCS 4622. Berlin: Springer-Verlag, 2007. 1–12Google Scholar
- 9.Matsumoto T, Imai H. Public quadratic polynomial-tuples for efficient signature verification and message encryption. In: Advances in Eurocryp1988, LNCS 330. Berlin: Springer, 1988. 419–453Google Scholar
- 10.Patarin J. Hidden field equations (HFE) and isomorphisms of polynomials (IP): two new families of asymmetric algorithms. In: Eurocrypt1996, LNCS 1070. Berlin: Springer, 1996. 33–48Google Scholar
- 11.Kipnis A, Patarin J, Goubin L. Unbalanced oil and vinegar signature schemes. In: EUROCRYPT 1999, Vol. 1592 of Lecture Notes in Computer Science. Berlin: Springer, 1999. 206–222Google Scholar
- 12.Yang B Y, Chen J M. Ranks attacks and defence in Tame-like multivariate PKCs. Report 2004/061, 29rd September 2004. http://eprint.iac.org
- 13.Patarin J. Cryptanalysis of the Matsumoto and Imai public key scheme of Eurocrypt 1988. In: Crypto1995, LNCS 963. Springer-Verlag, 1995. 248–261Google Scholar
- 14.Dubois V, Fouque P A, Stern J. Cryptanalysis of SFLASH with slightly modified parameters. In: Eurocrypt2007, LNCS 4145. Berlin: Springer-Verlag, 2007. 264–275Google Scholar
- 15.Patarin J, Goubin L, Courtois N. C−+* and HM: Variations around two schemes of T. Matsumoto and H. Imai. In: Asiacrypt1998, LNCS 1514. Berlin: Springer, 1998. 35–49Google Scholar
- 16.Gilbert H, Minier M. Cryptanalysis of SFLASH. In: Eurocrypt 2002, LNCS 2332. Berlin: Springer, 2002. 288–298CrossRefGoogle Scholar
Copyright information
© Science China Press and Springer-Verlag Berlin Heidelberg 2010