中文摘要：

RSA密码算法的实现电路易受到诸如能量分析、时间分析等旁门攻击。综述了RSA密码算法中模幂运算的主要攻击方法及其防御措施。针对模幂运算的软件实现和硬件实现，提出了基于随机概率的软件实现防御措施和基于模幂指数三进制表示的硬件实现防御措施。两种防御措施较之前的防御措施在安全性和效率方面都有显著的提高。两种防御措施具有通用性，可移植到ECC中的标量乘法运算中去。

英文摘要：

The implementation of RSA cryptosystems is vulnerable to SCA attacks such as power analysis and time attack. First countermeasures for the exponentiation computation of RSA cryptographic algorithm were summarized. Then the software countermeasures based on random probability and hardware countermeasure based on the 3-adic representation of exponent were proposed. Analysis shows that the two countermeasures achieved great improvements in both security and efficiency compared to existed countermeasures. Both two generic countermeasures can be transplanted to the scalar multiplication of ECC.