Efficient elliptic curve exponentiation

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.

• Type: Conference
• Year: 1997
• Where: ICICS
• Authors: Atsuko Miyaji, Takatoshi Ono, Henri Cohen
• Keywords: Communications, Elliptic Curve Cryptosystems, Fast Elliptic Curve, ICICS 1997, Smaller Definition Field