International Association
for Cryptologic Research

In this paper we introduce new methods for computing constant-time variable-base point multiplications over the Galbraith-Lin-Scott (GLS) and the Koblitz families of elliptic curves. Using a left-to-right double-and-add and a right-to-left halve-and-add Montgomery ladder over a GLS curve, we present some of the fastest timings yet reported in the literature for point multiplication. In addition, we combine these two procedures to compute a multi-core protected scalar multiplication. Furthermore, we designed for the first time a regular $\\tau$-adic scalar expansion for Koblitz curves. As a result, using the regular recoding approach, we set the speed record for a single constant-time point multiplication on standardized binary elliptic curves at the $128$-bit security level.