In this paper, we propose a binary modular exponentiation RSA countermeasure in order to defend against the comparative power analysis by dividing the private key e into n random parts and randomly choosing one of the parts to do one unit operation each selection till the modular exponentiation of all parts are completed. When the bit length of the private key computed actually is less than 4/3 of the original bit length of the private key, our method is more efficient and has more probability to against the exhaustive attack than the squaring-and-multiply-always right-to-left binary method which was previously considered to be the only effective binary method against the comparative power analysis. Further, the efficiency and security of our algorithm can be improved even more by adopting the parallel computing architecture.
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