Abstract
Straightforward implementations of binary exponentiation algorithms make the cryptographic system vulnerable to side-channel attacks; specifically, to simple power analysis (SPA) attacks. Solutions proposed so far introduce a considerable performance penalty. In this paper, we present a new method that implements an SPA-resistant binary exponentiation exhibiting optimal execution time at the cost of a small amount of storage—\({O(\sqrt{\ell})}\), where ℓ is the bit length of the exponent. The technique is optimal in the sense that it adds SPA-resistance to an underlying binary exponentiation algorithm while introducing zero computational overhead. Furthermore, we show that for practical applications, the same optimal execution time can be achieved with much less storage space, without noticeably sacrificing security or any other aspect of the cryptosystem’s performance. We also discuss the possibility of our method being implemented in a way that a certain level of resistance against differential power analysis may be obtained.
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Moreno, C., Hasan, M.A. SPA-resistant binary exponentiation with optimal execution time. J Cryptogr Eng 1, 87–99 (2011). https://doi.org/10.1007/s13389-011-0008-9
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DOI: https://doi.org/10.1007/s13389-011-0008-9