Normal basis multiplication and inversion unit for elliptic curve cryptography

Abstract

A design of a scalable arithmetic unit for operations over elements of GF(2/sup m/) represented in normal basis is presented. The unit is applicable in public-key cryptography. It comprises a pipelined Massey-Omura multiplier and a shifter. We equipped the multiplier with additional data paths to enable easy implementation of both multiplication and inversion in one arithmetic unit. We discuss optimum design of the shifter with respect to inversion algorithm and multiplier performance. The functionality of the multiplier/inverter has been tested by simulation and implemented in Xilinx Virtex FPGA. We present implementation data for various digit widths which exhibit a time minimum for digit width D=15.