Efficient Elliptic Curve Exponentiation Using Mixed Coordinates

  • Henri Cohen
  • Atsuko Miyaji
  • Takatoshi Ono
Conference paper

DOI: 10.1007/3-540-49649-1_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1514)
Cite this paper as:
Cohen H., Miyaji A., Ono T. (1998) Efficient Elliptic Curve Exponentiation Using Mixed Coordinates. In: Ohta K., Pei D. (eds) Advances in Cryptology — ASIACRYPT’98. ASIACRYPT 1998. Lecture Notes in Computer Science, vol 1514. Springer, Berlin, Heidelberg


Elliptic curve cryptosystems, proposed by Koblitz ([12]) and Miller ([16]), can be constructed over a smaller field of definition than the ElGamal cryptosystems ([6]) or the RSA cryptosystems ([20]). This is why elliptic curve cryptosystems have begun to attract notice. In this paper, we investigate efficient elliptic curve exponentiation. We propose a new coordinate system and a new mixed coordinates strategy, which significantly improves on the number of basic operations needed for elliptic curve exponentiation.

key words

elliptic curve exponentiation coordinate system 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Henri Cohen
    • 1
  • Atsuko Miyaji
    • 2
  • Takatoshi Ono
    • 3
  1. 1.Laboratoire A2XUniversit“é Bordeaux IUSA
  2. 2.Multimedia Development CenterMatsushita Electric Industrial Co., Ltd.USA
  3. 3.Matsushita Information Systems Research Laboratory Nagoya Co., Ltd.USA

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