Efficient elliptic curve exponentiation

  • Atsuko Miyaji
  • Takatoshi Ono
  • Henri Cohen
Session 9: Public Key Systems I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1334)


Elliptic curve cryptosystems, proposed by Koblitz([8]) and Miller([11]), can be constructed over a smaller definition field than the ElGamal cryptosystems([5]) or the RSA cryptosystems( [16]). This is why elliptic curve cryptosystems have begun to attract notice. There are mainly two types in elliptic curve cryptosystems, elliptic curves E over IF2r and E over IFp. Some current systems based on ElGamal or RSA may often use modulo arithmetic over IFp. Therefore it is convenient to construct fast elliptic curve cryptosystems over IFp. In this paper, we investigate how to implement elliptic curve cryptosystems on E/IFp.


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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Atsuko Miyaji
    • 1
  • Takatoshi Ono
    • 2
  • Henri Cohen
    • 3
  1. 1.Multimedia Development CenterMatsushita Electric Industrial Co., LTDJapan
  2. 2.Matsushita Information Systems Research Laboratory Nagoya Co., Ltd.Japan
  3. 3.Université de BordeauxJapan

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