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

Authors:
Brian Baldwin;Richard Moloney;Andrew Byrne;Gary Mcguire;William P. Marnane
Affiliations:
Claude Shannon Institute for Discrete Mathematics, Coding and Cryptography, and Dept. of Electrical & Electronic Engineering, University College Cork, Cork, Ireland;Claude Shannon Institute for Discrete Mathematics, Coding and Cryptography, and Dept. of Mathematics, University College Dublin, Dublin, Ireland;Dept. of Electrical & Electronic Engineering, University College Cork, Cork, Ireland;Claude Shannon Institute for Discrete Mathematics, Coding and Cryptography, and Dept. of Mathematics, University College Dublin, Dublin, Ireland;Claude Shannon Institute for Discrete Mathematics, Coding and Cryptography, and Dept. of Electrical & Electronic Engineering, University College Cork, Cork, Ireland
Venue:
ARC '09 Proceedings of the 5th International Workshop on Reconfigurable Computing: Architectures, Tools and Applications
Year:
2009

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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. Power analysis secure versions of both algorithms are also examined and compared. To the authors' knowledge, this work introduces the first documented FPGA implementation for computations on twisted Edwards curves over fields GF (p ).