A scalable and unified multiplier architecture for finite fields GF(p) and GF(2m)

Abstract

We describe a scalable and unified architecture for a Montgomery multiplication module which operates in both types of finite fields GF(p) and GF(2m). The unified architecture requires only slightly more area than that of the multiplier architecture for the field GF(p). The multiplier is scalable, which means that a fixed-area multiplication module can handle operands of any size, and also, the wordsize can be selected based on the area and performance requirements. We utilize the concurrency in the Montgomery multiplication operation by employing a pipelining design methodology. The upper limit on the precision of the scalable and unified Montgomery multiplier is dictated only by the available memory to store the operands and internal results, and the module is capable of performing in finite-precision Montgomery multiplication in both types of finite fields. © Springer-Verlag Berlin Heidelberg 2000.