Breaking randomized mixed-radix scalar multiplication algorithms

Abstract

In this paper we present a novel, powerful attack on a recently introduced randomized scalar multiplication algorithm based on covering systems of congruences. Our attack can recover the whole key with very few traces, even when those only provide partial information on the sequence of operations. In an attempt to solve the issues raised by the broken algorithm, we designed a constant-time version with no secret dependent branching nor memory access based on the so-called mixed-radix number system. We eventually present our conclusions regarding the use of mixed-radix representations as a randomization setting.