Efficient Signature Schemes Based on Polynomial Equations (preliminary version)

  • H. Ong
  • C. P. Schnorr
  • A. Shamir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 196)


Signatures based on polynomial equations modulo n have been introduced by Ong, Schnorr, Shamir [3]. We extend the original binary quadratic OSS-scheme to algebraic integers. So far the generalised scheme is not vulnerable by the recent algorithm of Pollard for solving s 1 2 + k s 2 2 = m (mod n) which has broken the original scheme.


  1. 1.
    Diffie, W. and Hellman, M.: New Directions in Cryptography. IEEE, IT-22, (1976), 644–654.MathSciNetGoogle Scholar
  2. 2.
    Ong, H. and Schnorr, C.P.: Signatures Through Approximate Representations by Quadratic Forms. Advances in Cryptology: Proceedings of Crypto 83. Plenum Publ. New York 1984, 117–132.Google Scholar
  3. 3.
    Ong, H., Schnorr, C.P., and Shamir, A.: An Efficient Signature Scheme Based on Quadratic Equations. Proceedings of 16th ACM-Symp. of Theory of Computing, Washington (1984), p. 208–216.Google Scholar
  4. 4.
    Pollard, J.M.: Solution of x2 + ky2 ≡ m (mod n), with Application to Digital Signatures. Preprint 1984.Google Scholar
  5. 5.
    Rabin, M.O.: Probabilistic Algorithms in Finite Fields. SIAM J. on Computing 9 (1980), p. 273–280.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Rivest, R.L., Shamir, A. and Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystems. Comm. ACM 21 (1978) 120–126.zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Shamir, A.: Identity Based Cryptosystems & Signature Schemes. Proceedings of Crypto 84.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • H. Ong
    • 1
  • C. P. Schnorr
    • 1
  • A. Shamir
    • 2
  1. 1.Fachbereich MathematikUniversität FrankfurtFrankfurtGermany
  2. 2.Applied Mathematics DepartmentThe Weizman Institute of ScienceRehovotIsrael

Personalised recommendations