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为了研究以适应弱计算环境提高密码运算速度为目标而经过Montgomery和中国剩余定理等方法加速后RSA算法的密码时间相关安全性,论文分析了Montgomery模幂运算中额外约简的发生几率,输入参数与运行时间之间的关系,提出了改进的定时按位比特搜索攻击方法,选择密文输入,对比运算耗时差量定时,按位搜索RSA的秘密因子,并在深腾1800高性能集群平台上进行了有关实验.研究显示:改进后的RSA算法虽能较好地免疫于传统定时攻击,但是按位比特搜索方法理论上完全能够搜索出RSA的素因子秘密参量.图1,表2,参8.
In order to study the cryptanalysis time-dependent security of the RSA algorithm after the Montgomery and Chinese Remainder Theorem are used to improve the cryptographic computation speed in the weak computing environment, the thesis analyzes the probability of occurrence of additional reductions in the Montgomery modular exponentiation. The input parameters And the running time, an improved timing bit-bit-search attack method is proposed, the ciphertext input is selected, the operation time-consuming timing is contrasted, and the RSA secret factor is searched bit by bit. On the platform of Shen Teng 1800 high performance cluster The experimental results show that the improved RSA algorithm is immune to the traditional timing attacks, but the bit-bit search method can theoretically search out RSA prime factor secret parameters.Figure 1, Table 2, 8.