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The aim of Elliptic Curve Cryptosystems (ECC) is to achieve the same security level as RSA but with shorter key size. The basic operation in the ECC is scalar multiplication which is an expensive operation. In this paper, we focus on optimizing ECC scalar multiplication based on Non-Adjacent Form (NAF). A new algorithm is introduced that combines an Add-Subtract Scalar Multiplication Algorithm with NAF representation to accelerate the performance of the ECC calculation. Parallelizing the new algorithm shows an efficient method to calculate ECC. The proposed method has speed up the calculation up to 60% compared with the standard method.

Accelerate Performance for Elliptic Curve Scalar Multiplication based on NAF by Parallel Computing