基于250位模乘平台的Tate对最终模幂算法的改进

在只支持250bits模乘的硬件平台上，实现457bits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457bits最终模幂。

Improvement of Final Modular Exponentiation Algorithm in Tate Pairing Based on 250 Bits Modular Multiplication Platform

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.