一种改进的在Hessian曲线上计算Tate双线性对的算法

An improved algorithm for computing Tate pairings on Hessian curves

选择适当的椭圆曲线,对于快速部署和实现椭圆曲线密码系统具有重要的意义.由于Hessian形式的椭圆曲线可以运用并行算法快速实现点加和倍点运算,因此能够有效提高系统的实现效率.利用Hessian曲线上点的优良性质,简化了直线斜率的计算公式,优化了在Hessian曲线上计算Tate双线性对的算法.在其他运算量保持不变的前提下,改进后的算法使点加和倍乘运算的运算量分别降低13.43%和11.25%.

The choice of appropriate elliptic curve is important for rapidly deploying and implementing elliptic curve cryptography. Hessian Elliptic Curve improve the efficiency of the system because it can run parallel algorithms to compute point addition and point doubling. This property is used to simplify the computation of slope and optimize the algorithm of calculating Tate bilinear. Under the condition that other operations are the same, the improved al- gorithm respectively cuts down 13.43% and 11.25% operations on point addition and point doubling.