Randomizing Scalar Multiplication Using Exact Covering Systems of Congruences

In this paper we present a generic, uniformly randomized scalar multiplication algorithm based on covering systems of congruences, with built-in protections against various side-channel attacks. It has been tailored to resist a recent class of attacks called horizontal attacks. These very powerful attacks exploit some unsuspected weaknesses hidden in most, if not all, highly regular and constant time algorithms. We provide a thorough complexity analysis, several arguments to support its robustness and some encouraging numerical experiments.