二元域乘法器的研究

Research on Multiplier over Binary Field

特征为2的椭圆曲线密码的主要运算为标量乘运算,其中二元域的乘法运算性能是影响标量乘运算的重要因素。文章根据Karatsuba-Ofman算法,对256×256的二元域乘法器的实现作了理论分析,进而用速度面积乘积衡量了各种实现,并指出其中的最佳方案,为实际应用的选择提供了参考。并以集成电路的形式作了实现,并对结果进行分析。

The main operation of Elliptic Curve Cryptography over characteristic 2 finite field is scalar multiplication, the performance of which is mainly affected by performance of multiplication over binary field. Our research analyzes the multiplier with 256-bits inputs over binary field which is designed to conform to the Karatsuba-Ofman algorithm. The results of each implementation are compared by speed-area product. The best one is then concluded and the best choice of applications is recommended. At last, the muhiplier is implemented in the form of integrated circuits and the results are analyzed.