Faster Scalar Multiplication on the x-Line: Three-Dimensional GLV Method with Three-Dimensional Differential Addition Chains

摘要

On the quadratic twist of a GLV curve, we explore faster scalar multiplication on its x-coordinate system utilizing three-dimensional GLV method. We construct and implement two kinds of three-dimensional differential addition chains, one of which is uniform and the other is non-uniform but runs faster. Implementations show that at about 254-bit security level, the triple scalar multiplication using our second differential addition chains runs about 26% faster than the straightforward computing using Montgomery ladder, and about 6% faster that the double scalar multiplication using DJB chains.