Fast algorithms for elliptic curve cryptosystems over binary finite field

摘要

In the underlying finite field arithmetic of an elliptic curve cryptosystem, field multiplication is the next computational costly operation other than field inversion. We present two novel algorithms for efficient implementation of field multiplication and modular reduction used frequently in an elliptic curve cryptosystem defined over GF (2~n). We provide a complexity study of the two algorithms and present an implementation performance of the algorithms over GF (2~(167)).