Abstract: Elliptic curve cryptosystem(ECC) is a kind of public-key cryptosystem, and its speed lies on the speed of scalar multiplication arithmetic. It is very simple to implement scalar multiplication by hardware when normal basis is used to denote the elements of base finite field, but it is very wasteful when n is a big number. This paper, under the analysis of algorithms in different levels of ECC, designs a fast scalar multiplication implementation and interface associated with 8-CPU. The result of FPGA implemetation indicates that 14 544 logic elements is used, and the efficiency of scalar multiplication is 40.71 per second at the frequeny of 53.70MHz.

Key words: polynomial basic, elliptic curve, scalar multiplication

摘要： 椭圆曲线密码体制是一种基于代数曲线的公开密码体制，其曲线的标量乘速度决定了该密码体制的速度。正规基表示基域元素虽然利于硬件实现，但当n较大时会消耗大量的硬件资源。该文通过对椭圆曲线密码体制不同层次的算法进行分析，给出了具体的快速实现方案，并完成了与8位CPU的接口设计。FPGA实现结果表明，硬件消耗为14 544个逻辑单元，在频率为53.70 MHz时钟驱动下，运算速度为每秒40.71次。

关键词: 多项式基, 椭圆曲线, 标量乘法

CLC Number: 

• TP309