Volume 11, Number 17, October 2021

Fast Implementation of Elliptic Curve Cryptographic Algorithm on GF(3^M) Based on FPGA

  Authors

Tan Yongliang, He Lesheng, Jin Haonan and Kong Qingyang, Yunnan University, China

  Abstract

As quantum computing and the theory of bilinear pairings continue being studied in depth, elliptic curves on GF(3^m ) are becoming of an increasing interest because they provide a higher security. What’s more, because hardware encryption is more efficient and secure than software encryption in today's IoT security environment, this article implements a scalar multiplication algorithm for the elliptic curve on GF(3^m ) on the FPGA device platform. The arithmetic in finite fields is quickly implemented by bit-oriented operations, and then the computation speed of point doubling and point addition is improved by a modified Jacobia projection coordinate system. The final experimental results demonstrate that the structure consumes a total of 7518 slices, which is capable of computing approximately 3000 scalar multiplications per second at 124 Mhz. It has relative advantages in terms of performance and resource consumption, which can be applied to specific confidential communication scenarios as an IP core.

  Keywords

GF(3^m), Elliptic Curve Cryptography, Scalar Multiplication, FPGA, IoT Security