A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem

Abstract

This paper presents implementation results of a reconfigurable elliptic curve processor defined over prime fields $GF(p)$. We use this processor to compare a new algorithm for point addition and point doubling operations on the twisted Edwards curves, against a current standard algorithm in use, namely the Double-and-Add. Secure power analysis versions of both algorithms are also examined and compared. The algorithms are implemented on an FPGA, and the speed, area and power performance of each are then evaluated for various modes of circuit operation using parallel processing. To the authors\u27 knowledge, this work introduces the first documented FPGA implementation for computations on twisted Edwards curves over fields $GF(p)$