有关中国剩余定理在多个素数的RSA解密运算中的加速公式的论证以及加速效率的估算

The deduction of the accelerated formula and the efficiency estimating in a number of primes in RSA decryption algorithm with Chinese remainder theorem

RSA算法在公钥密码体制中占有重要的地位,它的计算效率与模幂运算的实现效率有着直接关联。本实验在基于使用中国剩余定理简化的RSA解密算法的条件下,给出多个素数情况下的解密通用公式,通过减少大量的模幂运算,迅速简单地恢复出原文。并给出了效率提升估算公式,通过估算求出加速效率,为确定使用多少个素数最为合适提供依据。

RSA algorithms play an important role in the public key cryptography.Its computational efficiency have an immediately correlation with the efficiency of modular exponentiation implementation.In this paper the general formula for multiple primes of RSA algorithm were given by reducing the number of modular exponentiation,recover the original simply and fast.A formula for estimating efficiency also was given to calculate the efficiency of acceleration by estimating,which can provide the basis for the most appropriate numbers for RSA.