基于余数系统蒙哥马利模乘器的RSA密码算法

RSA Cryptographic Algorithm Based on Montgomery Modular Multiplier of Remainder System

当前RSA密码算法无法实现RSA加解密阶段大数模乘运算,因此提出基于余数系统蒙哥马利模乘器的RSA密码算法。依据余数系统模计算性能优势,构建二进制数值表示形式与运算法则表达式。采用Xilinx Virtex-Ⅱ平台与双模式乘法器,创建余数系统蒙哥马利模乘器硬件部分,通过四状态调度控制器控制模乘器。基于模乘器算术逻辑单元,完成算法中的乘法与乘累加运算。根据蒙哥马利模乘去除取模阶段的除法运算形式,运用模乘因子界定基转换算法,并采取一种近似方法将除法运算替换为移位操作,依据数据依赖关系对算法性能与芯片面进行折中处理,通过改变特殊基完成RSA密码算法构建。仿真结果表明,研究算法素数采集速率与加密速率高,算法执行时间短,加密效果更好。

At present,RSA encryption algorithm cannot realize the large number modular multiplication in the RSA encryption and decryption stage,so this paper proposes an RSA encryption algorithm based on the Montgomery modular multiplier of the remainder system.According to the advantages of the residual system,the binary numerical representation and algorithm expression were constructed.Using Xilinx Virtex-II platform and dual-mode multiplier,the hardware part of Montgomery modular multiplier of remainder system was created,and the modular multiplier was controlled by four state scheduling controller.Based on the arithmetic logic unit of modular multiplier,the multiplication and multiplication accumulation operations in the algorithm were completed.According to the division operation form of Montgomery's modular multiplication in the stage of removing modulus,the base conversion algorithm was defined by modular multiplication factor,and the division operation was replaced by shift operation based on an approximate method.The algorithm performance and chip surface were compromised according to the data dependence,and the RSA cryptographic algorithm was constructed by changing the special base.Simulation results show that the research algorithm has high prime acquisition rate and encryption rate,short algorithm execution time and better encryption effect.