超椭圆曲线上Weil对的变种与计算

摘要

To improve the computational efficiency of bilinear pairing, the optimal variation of Weil pairing was constructed using the self-isomorphic and highly twisted hyper-elliptic curves.It was proved that the optimal variation of Weil was a bilinear pairing by a series of proof.A new Miller algorithm was constructed based on the optimized variants of Weil pairing, which reduced the computation of the loop length of the Miller algorithm significantly and simplified the final exponentiation calculation of the Miller algorithm.The results show that the constructed variation of Weil pairing is optimized on a number of highly twisted hyper-elliptic curves.%为提高双线性对的计算效率,利用自同构以及高度扭曲的超椭圆曲线构造优化变种的Weil对.通过对优化变种Weil对的一系列证明,验证其是一个双线性对;基于优化变种Weil对构造新的Miller算法,使计算双线性对的Miller算法的循环次数显著减少,简化Miller算法最后的幂运算.实验结果表明,在一些高度扭曲的超椭圆曲线上,构造变种的Weil对是最优化的.