Computing isogenies in \(\mathbb{F}_{2^n } \)

  • Reynald Lercier
Conference paper

DOI: 10.1007/3-540-61581-4_55

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1122)
Cite this paper as:
Lercier R. (1996) Computing isogenies in \(\mathbb{F}_{2^n } \). In: Cohen H. (eds) Algorithmic Number Theory. ANTS 1996. Lecture Notes in Computer Science, vol 1122. Springer, Berlin, Heidelberg

Abstract

Contrary to what happens over prime fields of large characteristic, the main cost when counting the number of points of an elliptic curve E over \(\mathbb{F}_{2^n } \)is the computation of isogenies of prime degree ℓ. The best method so far is due to Couveignes and needs asymptotically O(ℓ3) field operations. We outline in this article some nice properties satisfied by these isogenies and show how we can get from them a new algorithm that seems to perform better in practice than Couveignes's though of the same complexity. On a representative problem, we gain a speed-up of 5 for the whole computation.

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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Reynald Lercier
    • 1
    • 2
  1. 1.Laboratoire d'Informatique de l'École Polytechnique (LIX)Palaiseau cedexFrance
  2. 2.CELAR/SSIGBruzFrance

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