Advertisement

Cryptanalysis of Two Sparse Polynomial Based Public Key Cryptosystems

  • Feng Bao
  • Robert H. Deng
  • Willi Geiselmann
  • Claus Schnorr
  • Rainer Steinwandt
  • Hongjun Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1992)

Abstract

The application of sparse polynomials in cryptography has been studied recently. A public key encryption scheme EnRoot [4] and an identification scheme SPIFI [1] based on sparse polynomials were proposed. In this paper, we show that both of them are insecure. The designers of SPIFI proposed the modified SPIFI [2] after Schnorr pointed out some weakness in its initial version. Unfortunately, the modi fied SPIFI is still insecure. The same holds for the generalization of EnRoot proposed in [2].

References

  1. 1.
    W. Banks, D. Lieman and I. Shparlinski, “An Identification Scheme Based on Sparse Polynomials”, in Proceedings of PKC’2000, LNCS 1751, Springer-Verlag, pp. 68–74, 2000.Google Scholar
  2. 2.
    W. Banks, D. Lieman and I. Shparlinski, “Cryptographic Applications of Sparse Polynomials over Finite Rings”, to appear in ICISC’2000.Google Scholar
  3. 3.
    T. ElGamal. “A Public Key Cryptosystem and a Signature Scheme based on Discrete Logarithms”. IEEE Transactions on Information Theory, 31 (1985), 469–472.zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    D. Grant, K. Krastev, D. Lieman and I. Shparlinski, “A Public Key Cryptosystem Based on Sparse Polynomials”, in Proceedings of an International Conference on Coding Theory, Cryptography and Related Areas, LNCS, Springer-Verlag, pp. 114–121, 2000.Google Scholar
  5. 5.
    J. Hoffstein, D. Lieman and J. H. Silverman, “Polynomial Rings and Efficient Public Key Authentication”, Proceedings of the International Workshop on Cryptographic Techniques and E-Commerce, pp. 7–19, M. Blum and C. H. Lee, eds., July 5-8, 1999, Hong Kong. At the time of writing also available at the URL http://www.ntru.com/technology/tech.technical.htm.
  6. 6.
    J. Hoffstein, J. Pipher and J. H. Silverman, “NTRU: A Ring Based Public Key System”, Proceedings of ANTS III, Porland (1998), Springer-Verlag.Google Scholar
  7. 7.
    V. Miller, “Uses of Elliptic Curves in Cryptography”, in Advances in Cryptology-Crypto’85, LNCS 218, Springer-Verlag, pp. 417–426, 1986.Google Scholar
  8. 8.
    R. L. Rivest, A. Shamir, and L. Adleman, “A method for Obtaining Digital Signatures and Public-Key Cryptosystems”, Commun. ACM, vol. 21, no. 2, pp. 158–164, Feb. 1978.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Feng Bao
    • 1
  • Robert H. Deng
    • 1
  • Willi Geiselmann
    • 2
  • Claus Schnorr
    • 3
  • Rainer Steinwandt
    • 2
  • Hongjun Wu
    • 1
  1. 1.Kent Ridge Digital LabsSingapore
  2. 2.Institut für Algorithmen und Kognitive Systeme Arbeitsgruppen Computeralgebra & Systemsicherheit, Prof. Dr. Th. BethUniversität KarlsruheKarlsruheGermany
  3. 3.Department of Mathematics/Computer ScienceJohann Wolfgang Goethe-UniversityFrankfurt am MainGermany

Personalised recommendations