基于FPGA的Fm2域椭圆曲线点乘的快速实现

摘要

The implementation speed of Elliptic Curve Cryptography (ECC) depends on the implementation speed of elliptic curve point multiplication.Point multiplication of elliptic curve using Montgomery algorithm was proposed in this paper.Parallel algorithm was used in modular multiplication algorithm and modular square algorithm, as well as Fermat's Little Theorem was used and optimized in modular inversion, thus the fast operation of elliptic curve point multiplication was implemented.Synthesis and implementation were realized in a Xilinx device of XC5VLX220T.Through timing simulation, the clock frequency can achieve 40MHz.It takes only 14.9μs to carry out one point multiplication operation.%椭圆曲线点乘的实现速度决定了椭圆曲线密码算法(ECC)的实现速度.采用蒙哥马利点乘算法,其中模乘运算、模平方运算采用全并行算法,模逆运算采用费马·小定理并在实现中进行了优化,完成了椭圆曲线点乘的快速运算.采用Xilinx公司的Viaex-5器件族的XCV220T作为目标器件,完成了综合与实现.通过时序后仿真,其时钟频率可以达到40 MHz,实现一次点乘运算仅需要14.9μs.