模幂运算安全外包算法的新设计

New design of secure outsourcing algorithm of modular exponentiation

由于模幂运算的计算成本较高,资源有限的本地客户端可以将模幂运算外包给计算能力强大的云服务器。该算法主要研究形如u ^(a)(mod N)的模幂运算的外包算法,其中N是两个大素数的乘积。其利用欧拉定理设计了一个基于双服务器模型的模幂运算安全外包方案。在运算外包过程中,保证底数u、指数a,以及运算结果对两个服务器的隐私保护。通过安全、效率分析和实验仿真表明,相较于现有方案,新方案具有更好的执行效率和可验证性,在用户端的效率更高,且新方案的可验证概率为1。

On account of the high computational cost of modular exponentiation,the local clients with limited resources can delegate the modular exponentiation to the cloud servers with strong computing capacity.This paper mainly studied the outsourcing algorithm of the modular exponentiation like u^(a)(mod N),where N is the product of two large prime numbers.The method used Euler theorem to design a new modular exponentiation outsourcing scheme based on two servers model.In the process of computing and outsourcing,it guaranteed the privacy protection of base u,exponent a and calculation results for the two severs.The safety and efficiency analysis and experimental simulation show that compared with the existing schemes,the proposed new scheme has better execution efficiency and verifiability,the efficiency is higher on the client side,and the probability of verifiability of the new scheme is 1.