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In this paper, we study the parallel implementations of elliptic curve scalar multiplication over prime fields using signed binary representations. Our implementation speeds up the calculation of scalar multiplication in comparison with the standard case. We introduce parallel algorithms for computing elliptic curve scalar multiplication based on representing the scalar by the Complementary Recoding Technique (CRT) and the Direct Recording Method (DRM). Both implementations of the proposed algorithms show speed-ups reaching up to 60% in comparison with execution time for sequential cases of the algorithms. We find that ECC-DRM is faster than ECC-CRT in both parallel and sequential counterparts.

Speeding Up the Computation of Elliptic Curve Scalar Multiplication based on CRT and DRM