Scalable Normal Basis Arithmetic Unit for Elliptic Curve Cryptography

The design of a scalable arithmetic unit for operations over elements of GF(2(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 a single arithmetic unit. We discuss optimum design of the shifter with respect to the 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.