Fast Implementation of Signatures Based on Elliptic Curves : Cryptography Scheme

ECDSA and Pairing are two usages that involve elliptic curves and Cryptography. In this work, several implementations will be reviewed and analyzed in order to construct efficient algorithms. After the mathematical background is given, some representation of elliptic curves will be introduced, including the newest Edwards form coordinate system. The first part refers to ECDSA and its implementations. The second part refers to pairing based cryptography and its implementations.