GF(p)上椭圆曲线密码的并行基点选取算法研究*

提出一种GF(p)上椭圆曲线密码系统的并行基点选取算法,该算法由并行随机点产生算法和并行基点判断算法两个子算法组成,给出了算法性能的理论分析和实验结果.结果表明:各并行处理器单元具有较好的负载均衡特性;当执行并行基点判断算法,其标量乘的点加计算时间是点倍数计算时间的三倍时,算法的并行效率可达90%.因此该算法可用于椭圆曲线密码(Elliptic Curve Cryptography,ECC)中基点的快速选取,从而提高ECC的加/解密速度.

Research on Parallel Algorithm of Selecting Base Points of Elliptic Curve Cryptography over GF(p)

This paper proposed a parallel algorithm of selecting base points of elliptic curve cryptography(ECC) over GF(p).The proposed parallel algorithm was composed of two sub-algorithms: parallel finding the random points of the elliptic curve(EC) cryptography and parallel judging whether or not the random point was the base point.Next the performances were theoretically analyzed and the experiment results were also given.The results show: all processors have better load balance;when the ratio of the execution time of a point addition to that of a point doubling is 3 during computing the scalar multiplication,the parallel efficiency of the proposed algorithm is up to 90%.Therefore,the proposed parallel algorithm can be applied to speed the selection of the base point of the elliptic curve cryptography over GF(p),improving the speed of encryption and decryption of ECC.