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Elliptic curve based cryptosystem is an efficient public key cryptosystem, which is more suitable for limited environments. The performance of elliptic curve cryptosystem heavily depends on an operation called point multiplication. The paper gives an introduction to Elliptic Curve Cryptography (ECC). The paper presents the comparative study of methods for point multiplication operation. In this paper, the authors have examined that the NAF method is efficient than the binary method as this improves the speed of the scalar multiplication. The paper also discusses the implementation of ECC on two finite fields, prime field and binary field.
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