摘要： 在椭圆曲线密码体制中，有限域的乘法运算是最关键的运算。基于II型正规基域的加法运算速度快、乘方运算简单，但乘法运算比较复杂，成为该域上运算的瓶颈。为了解决这个问题，该文在分析串行乘法算法的基础上对算法进行改进，该算法与串行乘法算法相比，减少了运算周期，有效地提高了运行速度，根据改进算法设计并行乘法器结构，并在FPGA上进行实现，为进一步提高椭圆曲线加密速度提供硬件基础。

关键词: 有限域, 正规基, 椭圆曲线, 乘法器

Abstract: Multiplication operation over the finite field is the most crucial part in the elliptic curve cryptosystems. It operates a faster addition and simpler square with the elements representing on the finite field, but the comparison of the multiplication has become the bottleneck of operation. To solve this problem, This paper puts forward a modified scheme based on analyzing serial multiplication, with which compared the scheme reduces the operation cycles greatly, enhances the speed efficiently, and designs the parallel multiplier structure based on the modified scheme. This paper implements the modified scheme on FPGA, and lays hardware basis on improving elliptic curve encryption speed.

Key words: finite field, normal basis, elliptic curve, multiplicatier

中图分类号: 

• TP309.2