Same Values Power Analysis Using Special Points on Elliptic Curves

Elliptic Curve Cryptosystems (ECC) on Smart-Cards can be vulnerable to Side Channel Attacks such as the Simple Power Analysis (SPA) or the Differential Power Analysis (DPA) if they are not carefully implemented. Goubin proposed a variant of the DPA using the point (0, y ). This point is randomized neither by projective coordinates nor by isomorphic class. Akishita and Takagi extended this attack by considering not only points with a zero coordinate, but also points containing a zero value on intermediate registers during doubling and addition formulas. This attack increases the number of possible special points on elliptic curve that need a particular attention. In this paper, we introduce a new attack based on special points that show up internal collision power analysis. This attack increases more the number of possible special points on elliptic curve that need a particular attention. Like Goubin's attack and Akishita and Takagi's attack, our attack works if a fixed scalar is used and the attacker can chose the base point.

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