Design of Parallel Pipelined Algorithm for Field Arithmetic Architecture Based on Cellular Array

摘要

In this study, we present an efficient finite field arithmetic algorithm for multiplication which is a core algorithm for division and exponentiation operations. In order to obtain a dedicated pipelined algorithm, we adopt Montgomery algorithm and cellular systolic array. First of all, we select an effective Montgomery factor for the design of our parallel algorithm, then we induce an efficient multiplication algorithm from the typical binary MM algorithm using the factor. In this paper, we show the detail derivation process in order to obtain the recursive equations for pipelined computation.