A Public Key Cryptosystem Based on Elliptic Curves over ℤ/nℤ Equivalent to Factoring

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1070)


Elliptic curves over the ring ℤ/nℤ where n is the product of two large primes have first been proposed for public key cryptosystems in [4]. The security of this system is based on the integer factorization problem, but it is unknown whether breaking the system is equivalent to factoring. In this paper, we present a variant of this cryptosystem for which breaking the system is equivalent to factoring the modulus n. Moreover, we extend the ideas to get a signature scheme based on elliptic curves over ℤ/nℤ.


Elliptic Curve Signature Scheme Elliptic Curf Chinese Remainder Theorem Decryption Procedure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    M. Joye, J.-J. Quisquater: Personal communication Google Scholar
  2. 2.
    M. Joye, J.-J. Quisquater: Note on the public-key cryptosystem of Meyer and Müller, Technical Report CG-1996/2, Université catholique de LouvainGoogle Scholar
  3. 3.
    N. Koblitz: Elliptic curve cryptosystems, Mathematics of Computation, 48 (1987), 203–209CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    K. Koyama, U. Maurer, T. Okamoto, S. Vanstone: New Public-Key Schemes Based on Elliptic Curves over the Ringn, Advances in Cryptology: Proceedings of Crypto’ 91, Lecture Notes in Computer Science, 576 (1991), Springer-Verlag, 252–266Google Scholar
  5. 5.
    K. Kurosawa, K. Okada, S. Tsujii: Low exponent attack against elliptic curve RSA, Advances in Cryptology-ASIACRYPT’ 94, Lecture Notes in Computer Science, 917 (1995), Springer-Verlag, 376–383CrossRefGoogle Scholar
  6. 6.
    A. Menezes: Elliptic Curve Public Key Cryptosystems, Kluwer Academic Publishers (1993)Google Scholar
  7. 7.
    V. Miller: Uses of elliptic curves in cryptography, Advances in Cryptology: Proceedings of Crypto’ 85, Lecture Notes in Computer Science, 218 (1986), Springer-Verlag, 417–426CrossRefGoogle Scholar
  8. 8.
    V. Shoup: A New Polynomial Factorization Algorithm and its Implementation, Preprint, (1995)Google Scholar
  9. 9.
    J. H. Silverman: The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 106, Springer-Verlag, (1986)Google Scholar
  10. 10.
    H. C. Williams: A modification of the RSA public-key encryption procedure, IEEE Transactions on Information Theory, IT-26, No. 6, (1980), 726–729CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  1. 1.Fachbereich InformatikUniversität des SaarlandesSaarbrückenGermany
  2. 2.Department of Combinatorics & OptimizationUniversity of WaterlooWaterlooCanada

Personalised recommendations