Another Look at Inversions over Binary Fields

Abstract

In this paper we offer new algorithms for one of the most common operations in public key cryptosystems: the inversion over binary Galois fields. The new algorithms are based on using double-base and triple-base representations. They are provably more economical-in terms of the average number of multiplications-than the popular Itoh-Tsujii algorithm. In addition to having fewer multiplications, the new inversion algorithms offer further implementation advantages because they allow more efficient computation of squarings and, in some cases, require fewer temporary variables. The new algorithms are straightforwardly usable in both software and hardware implementations.