Scalable Normal Basis Arithmetic Unit for Elliptic Curve Cryptography

J. Schmidt, M. Novotný


The design of a scalable arithmetic unit for operations over elements of GF(2m) 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.


finite fields; normal base; multiplication; inversion; arithmetic unit

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ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague