Advertisement

A Rabin-type scheme based on y2x3 + bx2 mod n

  • Seng Kiat Chua
  • San Ling
Session 6: Cryptography and Computational Finance
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1276)

Abstract

We propose a new Rabin-type scheme, based on y2x3 + bx2 mod n, that extends a scheme proposed by Meyer and Müller based on elliptic curves. The new scheme has security also equivalent to factorisation of n, seems easier in implementation and does not depend on probabilistic algorithms.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    K. Koyama, Fast RSA-type schemes based on singular cubic curves y 2 + axyx 3 (mod n), in Advances in Cryptology-Proceedings of Eurocrypt'95, Lecture Notes in Computer Science 921 (Springer-Verlag, 1995), 329–339Google Scholar
  2. 2.
    K. Koyama, U.M. Maurer, T. Okamoto & S.A. Vanstone, New public-key schemes based on elliptic curves over the ringn, in Advances in Cryptology-Proceedings of Crypto'91, Lecture Notes in Computer Science 576 (Springer-Verlag, 1992), 252–266Google Scholar
  3. 3.
    H. Kuwakado, K. Koyama & Y. Tsuruoka, A new RSA-type scheme based on singular cubic curves y 2x 3 + bx 2 (mod n), IEICE Trans. Fund. E78-A (1995), 27–33Google Scholar
  4. 4.
    B. Meyer & V. Müller, A public key cryptosystem based on elliptic curves over ℤ/nequivalent to factoring, in Advances in Cryptology-Proceedings of Eurocrypt'96, Lecture Notes in Computer Science 1070 (Springer-Verlag, 1996), 49–59Google Scholar
  5. 5.
    M. Joye & J.-J. Quisquater, On the cryptosystem of Chua and Ling, UCL Crypto Group Technical Report, CG-1997/4, Apr. 1997Google Scholar
  6. 6.
    M. Joye & J.-J. Quisquater, Reducing the elliptic curve cryptosystem of Meyer-Müller to the cryptosystem of Rabin-Williams, to appear in Designs, Codes and CryptographyGoogle Scholar
  7. 7.
    M.O. Rabin, Digitalized signatures and public-key functions as intractable as factorization, M.I.T. Technical Report, LCS/TR212, 1979Google Scholar
  8. 8.
    J.H. Silverman, The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics 106, Springer-Verlag, 1986Google Scholar
  9. 9.
    H.C. Williams, A modification of the RSA public-key encryption procedure, IEEE Transactions on Information Theory IT-26, No. 6 (1980), 726–729.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Seng Kiat Chua
    • 1
  • San Ling
    • 1
  1. 1.Department of MathematicsNational University of SingaporeSingaporeRepublic of Singapore

Personalised recommendations