Fast Algorithms for Arithmetic on Elliptic Curves Over Prime Fields

Nicholas T.  Sullivan

Paper 2008/060

Fast Algorithms for Arithmetic on Elliptic Curves Over Prime Fields

Nicholas T. Sullivan

Abstract

We present here a thorough discussion of the problem of fast arithmetic on elliptic curves over prime order ﬁnite ﬁelds. Since elliptic curves were independently pro- posed as a setting for cryptography by Koblitz [53] and Miller [67], the group of points on an elliptic curve has been widely used for discrete logarithm based cryptosystems. In this thesis, we survey, analyse and compare the fastest known serial and parallel algorithms for elliptic curve scalar multiplication, the primary operation in discrete logarithm based cryptosystems. We also introduce some new algorithms for the basic group operation and several new parallel scalar multiplication algorithms. We present a mathematical basis for comparing the various algorithms and make recommendations for the fastest algorithms to use in diﬀerent circumstances.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Thesis, University of Calgary, 2007
Keywords: Elliptic Curve Cryptography
Contact author(s): nicholas sullivan @ gmail com
History: 2008-02-11: received
Short URL: https://ia.cr/2008/060
License: CC BY

BibTeX

@misc{cryptoeprint:2008/060,
      author = {Nicholas T.  Sullivan},
      title = {Fast Algorithms for Arithmetic on Elliptic Curves Over Prime Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2008/060},
      year = {2008},
      url = {https://eprint.iacr.org/2008/060}
}