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Elliptic Curve Cryptography (ECC) is becoming widely deployed in embedded cryptographic devices. However, simple power analysis (SPA) attacks may retrieve secret keys by exploiting the power consumption of ECC devices. To resist the SPA attack there appear a number of countermeasures and the most widely used methods are Montgomery ladder and doubleand-add-always algorithm. This paper proposes a refined simple power analysis attack to these countermeasures. Experimental results on smart cards demonstrate that this attack method can retrieve secret keys by distinguishing the power consumption of different jump instructions if the implementation of ECC’s countermeasure is not carefully designed. The experiments also demonstrate that the proposed countermeasure in this paper can resist this kind of SPA attack. Keywords—ECC; cryptography; SPA; scalar multiplication

A Refined Simple Power Analysis Attack on ECC with Countermeasures