摘要：

R-ate是国密SM9标识密码算法中一种重要的双线性映射,其计算性能对SM9密码体制的应用至关重要。为提升R-ate双线性对的计算效率,提出一种快速计算算法。通过对BN曲线上R-ate双线性对的计算过程和其中涉及的逆运算原理进行分析,改变计算中同构映射的作用顺序,将大部分逆运算从大特征域转到小特征域,以降低逆元求解的计算损耗。以SM9的系统参数为计算实例进行实验,结果表明,该算法的运行时间低至1.8×105 ms。

关键词: 国密SM9, 双线性对, R-ate计算, 标识密码算法, 椭圆曲线对

Abstract:

R-ate is an important bilinear mapping in the Identity-Based Cryptography(IBC) algorithm of China state cryptography standard SM9.Its computational performance is very important to the application of SM9 cryptosystem.To improve the computational efficiency of R-ate bilinear pairing,a fast computational algorithm is proposed.By analyzing the computation process of R-ate bilinear pairing on BN curves and the involved principle of inverse operations,the order in which isomorphic mapping takes effect in computation is changed,and most of the inverse operations are transferred from the large feature domain to small feature domain to reduce the computation loss of inverse element solution.The system parameters of SM9 are taken as an example to carry out experiments.Results show that the running time of the proposed algorithm is only 1.8×105 ms.

Key words: China state cryptography standard SM9, bilinear pairing, R-ate computing, Identity-Based Cryptography(IBC) algorithm, elliptic curve pairing

中图分类号: 

• TP399