Finite Fields for Software Implementation of Elliptic Curve Cryptosystems

概要

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This paper identified a family of finite fields over which efficient elliptic curve cryptosystems can be obtained. Most reported elliptic curve cryptosystems are defined over finite fields of characteristic two i. e. GF (2^n). It is widely believed that elliptic curves defined over such finite fields can have more efficient implementation hardware. Furthermore, the fastest software implementation reported to date is also based on curves defined over such fields. In this paper, we show that GF (2^n) is not the most suitable field for software implementation. We identified a family of finite fields of the form GF (2^n-s), where 2^n-s is a large prime and s is a random single precision integer, which is more suitable for software implementation of elliptic curve cryptosystems. Experimental results on some popular software implementation platforms including DEC Alpha, SUN SPARC and Intel Pentium show that we can achieve faster software implementation of the group addition and scalar multiplication of elliptic curve over finite field GF (2^n-s) than over the field GF (2^n).
社団法人電子情報通信学会の論文
1998-12-11