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Title:
Revisiting Atomic Patterns for Scalar Multiplications on Elliptic Curves
Authors: Franck Rondepierre
Abstract:This paper deals with the protection of elliptic curve scalar multiplications against side-channel analysis by using the atomicity principle. Unlike other atomic patterns, we investigate new formul\ae{} with same cost for both doubling and addition. This choice is particularly well suited to evaluate double scalar multiplications with the Straus-Shamir trick. Since fixed point multiplications highly benefit from this trick, our pattern allows a huge improvement in this case as other atomic patterns cannot use it. Surprisingly, in other cases our choice remains very efficient. Besides, we also point out a security threat when the curve parameter a is null and propose an even more efficient pattern in this case.
ePrint: https://eprint.iacr.org/2015/408
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