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

Brian Baldwin; Richard Moloney; Andrew Byrne; Gary McGuire; William P.  Marnane

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Paper 2009/001

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

Brian Baldwin, Richard Moloney, Andrew Byrne, Gary McGuire, and William P. Marnane

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' knowledge, this work introduces the first documented FPGA implementation for computations on twisted Edwards curves over fields $GF(p)$.

Note: The paper has been updated (approx +2 pages) to now include a more complete hardware section and also a hardware description of modular addition and Montgomery multiplication operation. None of this is included in the ARC09 version.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. To appear in ARC 2009, the 5th International Workshop on Applied Reconfigurable Computing
Keywords: Hardware elliptic curve cryptosystem Edwards curves FPGA
Contact author(s): brianb @ rennes ucc ie
History: 2009-01-04: received
Short URL: https://ia.cr/2009/001
License: CC BY

BibTeX

@misc{cryptoeprint:2009/001,
      author = {Brian Baldwin and Richard Moloney and Andrew Byrne and Gary McGuire and William P.  Marnane},
      title = {A Hardware Analysis of Twisted Edwards Curves for an Elliptic Curve Cryptosystem},
      howpublished = {Cryptology ePrint Archive, Paper 2009/001},
      year = {2009},
      note = {\url{https://eprint.iacr.org/2009/001}},
      url = {https://eprint.iacr.org/2009/001}
}