基于250位模乘平台的 Tate 对最终模幂算法的改进

摘要

在只支持250 bits模乘的硬件平台上，实现457 bits的二元扩域Tate对Miller算法的（双线性对的一种）最终模幂运算。在计算过程中采用一种改进的Montgomery模乘算法和中国剩余定理算法。通过具体数据实现双线性对最终模幂的运算，使用数学软件Sage来验证这种改进方案的正确性。通过理论分析和数据计算可以证明使用该方案可实现457 bits最终模幂。%The purpose of this article is to realize the 457 bits final modular exponentiation in the Tate pairing Miller algorithm ( one kind of bilinear pairings ) of binary extension field on the hardware platform which only supports 250 bits modular multiplica-tion.In the procedure of calculation , we adopted an improved Montgomery modular multiplication algorithm and Chinese remain-der theorem algorithm .The final modular exponentiation will be realized with definite data , and we will use the mathematical soft-ware Sage to verify the improved scheme .So we can prove that this scheme can realize the 457 bits final modular exponentiation through theory analysis and data calculation .