二进制域滑动窗口快速模乘算法

加速GF（2^m）上的模乘运算是提高GF（2^m）上ECC算法性能的关键。分析了窗口宽度ω的comb多项式乘法和NIST约简多项式算法,结合两种算法提出一种滑动窗口的快速模乘算法。该算法弥补了先乘后模方法在时间上和存储空间上的缺点,缩短了运算时间,仿真结果表明快速模算法的运算效率比先乘后模的窗口comb多项式乘法和NIST快速约简速度提高21%左右,预计算只需要ω-1个值。

Fast modular multiplication of sliding window based on binary domain

Speeding up the modular multiplication holds the key to improving the performances of ECC algorithms in GF（2^m）.This paper presents an analysis of the comb polynomial multiplication（windows of width ω）and NIST reduction polynomials and features a faster modular multiplication algorithm of sliding window by combining the two operations.The algorithm can reduce the computing time by overcoming the shortcomings of modular-after-multiplication in time and storage space.The analysis of mathematic modeling and simulating shows that the new algorithms features computation efficiency about 21 percent greater than former modular-after-multiplication and NIST reduction polynomials and only ω-1 values are needed in pre-computation.