I. Introduction
Elliptic curve cryptography (ECC) was first proposed by Miller and Koblitz in 1985 [1]. In virtue of no subexponential algorithms known for the elliptic-curve discrete-logarithm problem (ECDLP), ECC provides equivalent security strengths with shorter keys compared to other public-key cryptosystems. Due to this advantage, ECC has acquired wide attention in academia as well as industry.