Generating Elliptic Curves of Prime Order

  • Erkay Savaş
  • Thomas A. Schmidt
  • Çetin K. Koç
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2162)


A variation of the Complex Multiplication (CM) method for generating elliptic curves of known order over finite fields is proposed. We give heuristics and timing statistics in the mildly restricted setting of prime curve order. These may be seen to corroborate earlier work of Koblitz in the class number one setting. Our heuristics are based upon a recent conjecture by R. Gross and J. Smith on numbers of twin primes in algebraic number fields.

Our variation precalculates class polynomials as a separate off-line process. Unlike the standard approach, which begins with a prime p and searches for an appropriate discriminant D, we choose a discriminant and then search for appropriate primes. Our on-line process is quick and can be compactly coded.

In practice, elliptic curves with near prime order are used. Thus, our timing estimates and data can be regarded as upper estimates for practical purposes.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Erkay Savaş
    • 1
  • Thomas A. Schmidt
    • 2
  • Çetin K. Koç
    • 1
  1. 1.Department of Electrical & Computer EngineeringOregon State UniversityCorvallisUSA
  2. 2.Department of MathematicsOregon State UniversityCorvallisUSA

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