Atomicity Improvement for Elliptic Curve Scalar Multiplication

Abstract: In this paper we address the problem of protecting elliptic curve scalar multiplication implementations against side-channel analysis by using the atomicity principle. First of all we reexamine classical assumptions made by scalar multiplication designers and we point out that some of them are not relevant in the context of embedded devices. We then describe the state-of-the-art of atomic scalar multiplication and propose an atomic pattern improvement method. Compared to the most efficient atomic scalar multiplication published so far, our technique shows an average improvement of up to 10.6%.