Generating anomalous elliptic curves

  • Authors:

  • Franck Leprévost;Jean Monnerat;Sébastien Varrette;Serge Vaudenay

  • Affiliations:

  • Université du Luxembourg, LIASIT, 162 A, Avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg;EPFL, LASEC, CH-1015 Lausanne, Switzerland;Université du Luxembourg, LIASIT, 162 A, Avenue de la Faïencerie, L-1511 Luxembourg, Luxembourg;EPFL, LASEC, CH-1015 Lausanne, Switzerland

  • Venue:
  • Information Processing Letters
  • Year:
  • 2005

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Abstract

In 1999, Smart has shown how to solve in linear time ECDLP for elliptic curves of trace 1 defined over a prime finite field F"p, the so-called anomalous elliptic curves. In this article, we show how to construct such cryptographically weak curves for primes p of industrial length, using complex multiplication theory.