An alternate approach to modular multiplication for finite fields [GF (2/sup m/)] using Itoh Tsujii algorithm

Abstract

Modular arithmetic operations especially modular multiplication have extensive applications in elliptic curve cryptanalysis, error control coding and linear recurring sequences. These operations have steadily grown in the word size in the past. Current designs and approaches may not be the most efficient for such high word sizes. Also usually, most approaches optimize for either area or speed, not both. In this paper, we examine certain properties and elucidate certain alternative strategies of and on the Itoh Tsujii algorithm (Guajardo and Paar, 2002) that will make it suitable for this emerging scenario. These strategies take a holistic approach to the problem, and aims at optimizing both speed and area for a given word length. These claims are supported by mathematical analysis, simulation and synthesis of a prototype of the suggested strategy. We also examine various enhancements that can be effected in the given architecture.