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Elliptic Curve Cryptography is gaining attraction in providing a high security level in data transmission with low cost, small key size and smaller hardware realization. High-speed implementation is a significant factor in ECC applications such as smart cards, network servers, wireless sensor based networks, Internet of Things and Radio Frequency Identification. These applications require low-cost and lightweight implementations. In the resource constrain application, lightweight cryptography has emerged as the desired one because of limited energy in devices and the scarce computational resources. Design options and a wide range of parameters affect the overall implementation of the ECC system. Implementation target device, coordinate system, underlying finite fields and modular arithmetic algorithms are key design parameters that impact the overall implementation outcome. A statistical study is conducted on a large collection of published work based on the design parameters. The basic question that arises is how to select the appropriate flexibility-efficiency tradeoff. The subjects of generator, versatile, reconfigurable, dedicated and general purpose scalar multipliers are addressed. A review of various algorithms to perform scalar multiplication on prime and binary fields has been done more effectively. The results of ECC implementation on different FPGA platform is compared and analyzed with the various performance parameters. Besides, a classification of the previous works in terms of flexibility, performance, scalability and cost effectiveness is presented.

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