A scalable structure for a multiplier and an inversion unit in GF(2(m))

Abstract

Elliptic curve cryptography (ECC) offers the highest security per bit among the known public key cryptosystems. The operation of ECC is based on the arithmetic of the finite field. This paper presents the design of a 193-bit finite field multiplier and an inversion unit based on a normal basis representation in which the inversion and the square operation units are easy to implement. This scalable multiplier can be constructed in a variable structure depending on the performance area trade-off. We implement it using Verilog HDL and a 0.35 mum CMOS cell library and verify the operation by simulation.