Parallel Method for Computing Elliptic Curve Scalar Multiplication Based on MOF

This paper focuses on optimizing the Elliptic Curve Cryptography (ECC) scalar multiplication by optimizing one of the ECC calculations, which is based on the Mutual Opposite Form (MOF) algorithm. A new algorithm is introduced that combines the add-subtract scalar multiplication algorithm with the MOF representation to speed-up the ECC scalar multiplication. The implementation of the algorithm produces an efficient parallel method that improves the computation time. The proposed method is an efficient ECC scalar multiplication that achieves a 90% speed-up compared to the existing methods.