Software implementation of finite fields in characteristic three

Abstract. In this paper we examine a number of ways of implementing characteristic three arithmetic in hardware. While this type of arithmetic is not traditionally used in cryptographic systems, recent advances in Tate and Weil pairing based cryptosystems show that it is potentially valuable. We examine a hardware oriented representation of the field ele-ments, comparing the resulting algorithms for field addition and multipli-cation operations, and show that characteristic three arithmetic need not significantly under-perform comparable characteristic two alternatives.