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
Index Terms-Hyper elliptic curve, ECDLP,Montgomery prime, Kummer surface.