Modular multiplication in GF(pk) using Lagrange representation

Abstract

In this paper we present a new hardware modular multiplication algorithm over the finite extension fields GF(pk) where p > 2k. We use an alternate polynomial representation of the field elements and a Lagrange like interpolation technique. We describe our algorithm in terms of matrix operations and point out some properties of the matrices that can be used to improve the hardware design. The proposed algorithm is highly parallelizable and seems well suited for hardware implementation of elliptic curve cryptosystems.