Specialized integer factorization

  • Don Coppersmith
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1403)


Vanstone and Zuccherato [3] propose a cryptographic system based on an elliptic curve modulo a composite number. We show that the composite numbers so constructed are easily factored, rendering the system insecure.


  1. 1.
    D. Coppersmith, “Finding a small root of a bivariate integer equation; factoring with high bits known,” Advances in Cryptology — EUROCRYPT '96, Ueli Maurer (Ed.), Springer LNCS Volume 1070, 1996, pages 178–189.MathSciNetGoogle Scholar
  2. 2.
    D. Coppersmith, “Small Solutions to Polynomial Equations, and Low Exponent RSA Vulnerabilities,” Journal of Cryptology, Volume 10 Number 4, Autumn 1997, pages 233–260.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    S. A. Vanstone and R. J. Zuccherato, “Elliptic curve cryptosystems using curves of smooth order over the ring Zn,” IEEE Trans. Inform. Theory, Volume IT-43, 1997, pages 1231–1237.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Don Coppersmith
    • 1
  1. 1.IBM Research T.J. Watson Research CenterYorktown HeightsUSA

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