High Performance Methods of Elliptic Curve Scalar Multiplication

Elliptic curve scalar multiplication is the operation of successively adding a point along an elliptic curve to itself k times. It is used in elliptic curve cryptography (ECC) as a means of producing a trapdoor function. In this paper, algorithms to compute the elliptic curve scalar multiplication using a special form for integers will introduce, and then two types of signed digit representation will use. The signed digit form of the scalar is calculated by many types of algorithms such as binary , non adjacent form and direct recoding. The results indicate that the proposed methods perform better to compute the scalar multiplication on elliptic curves and it is more efficient than the existing methods.