Classification and Comparison of Scalar Multiplication Algorithms in Elliptic Curve Cryptosystems

The most popular public-key cryptography systems nowadays are RSA and Elliptic Curve Cryptography (ECC). ECC is a type of public-key cryptosystem which uses the additive group of points on a nonsingular elliptic curve as a cryptographic medium. The basic operation in most elliptic curve cryptosystems is a scalar multiplication. Scalar Multiplication is the costliest operation among all in ECC which takes 80% of key calculation time on Elliptic curve calculation. Hence Scalar multiplication is the most time- consuming operation in ECC protocols. Scalar multiplication (or point multiplication) is the operation of calculating an integer multiple of an element in additive group of elliptic curve. in this paper, we classify and compare proposed scalar multiplication algorithms and compute their executing time.

Keywords:

ECC , Cryptography , Elliptic Curve , Scalar Multiplication