Parallel approaches for efficient scalar multiplication over elliptic curve

This paper deals with parallel implementation of scalar multiplication over an elliptic curve. We present parallel approaches which split the scalar into two parts for E(Fp) or three parts for E(F2m) and perform in parallel the scalar multiplication with each part of the scalar. We present timing results of these approaches implemented over an Intel Core i7 for NIST binary curves B233, B409 and for the twisted Edwards curve Curve25519 (Bernstein, 2006). For the curves B409 and Curve25519 the proposed approaches improve by at least 10% the computation time of the scalar multiplication.