A Comparative Study On Elliptic Curve Cryptography Methods

The elliptic curve cryptography recommends curves for different perceived security levels. These curves are either defined over prime fields or binary extension fields, however, the deployed elliptic curves are mostly defined over prime fields. The three curve based methods: Edward curve, Hyperelliptic curve and Weierstrass curve are analyzed based on the performance of the parameters. Consider both Montgomery multiplication and Kummer Surface which enhance the performance and gives more efficient to arithmetic operations. Hyperellipticcurve provide stronger and better security. The implementation shows fixed base scalar multiplication on Hyperelliptic curve is faster than Edward curve and Weierstrass curve. Index Terms-Hyper elliptic curve, ECDLP,Montgomery prime, Kummer surface.