Equivalence of counting the number of points on elliptic curve over the ring Zn and factoring n

  • Noboru Kunihiro
  • Kenji Koyama
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1403)


For composite n, we prove that counting the number of points on elliptic curves over the ring Zn is randomly computationally equivalent to factoring n. That is, we prove that if we can count it, we can easily factor n. Furthermore, we also prove that if we can solve the elliptic curve discrete logarithm problem modulo n, we can easily factor n.


Polynomial Time Prime Factor Elliptic Curve Elliptic Curf Zero Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Noboru Kunihiro
    • 1
  • Kenji Koyama
    • 1
  1. 1.NTT Communication Science LaboratoriesKyotoJapan

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