Cryptology ePrint Archive: Report 2005/419

Unified Point Addition Formulæ and Side-Channel Attacks

Douglas Stebila and Nicolas Thériault

Abstract: The successful application to elliptic curve cryptography of side-channel attacks, in which information about the secret key can be recovered from the observation of side channels like power consumption or timing, has motivated the recent development of unified formulæ for elliptic curve point operations. In this paper, we give a version of a previously-developed family of unified point addition formulæ that uses projective coordinates for improved efficiency. We discuss the applicability of a recent attack by Walter on this family of projective formulæ and describe how the field arithmetic can be implemented to obtain fully unified formulæ and avoid this type of attack.

Category / Keywords: public-key cryptography / elliptic curve cryptosystem

Date: received 18 Nov 2005

Contact author: ntheriau at math uwaterloo ca

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Version: 20051121:080648 (All versions of this report)

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