Public-key cryptography, or asymmetric cryptography, is a cryptosystem that uses two keys, public key and private key. Public key is released widely and private key is kept secret by the owner. Security of an asymmetric cryptosystem is based on an intractable problem like discrete logarithm problem, closet vector problem, and etc. In elliptic curve cryptosystem, one of the most important tasks is to select an appropriate key to have high security. In this process, one of the most crucial issues is the computation of scalar multiplication at the base point.
