Optimizing Elliptic Curve Scalar Multiplication with Near-Factorization

Elliptic curve scalar multiplication ( [k]P where k is an integer and P is a point on the elliptic curve) is widely used in encryption and signature generation. In this paper, we explore a factorization-based approach called Near-Factorization that can be used in conjunction with existing optimization techniques such as Window NAF (Non Adjacent Form). We present a performance model of Near-Factorization and validate model results with those from a simulation. We compare Near-Factorization with wNAF for a range of scalar sizes, window sizes, divisor lengths and Hamming weights of divisor. The use of Near-Factorization with wNAF results in a considerable reduction in the effective Hamming weight of the scalar and a reduction in overall computation cost for Koblitz curves.