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Fast Algorithms for Arithmetic on Elliptic Curves Over Prime Fields

Authors:
Nicholas T. Sullivan
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URL: http://eprint.iacr.org/2008/060
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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.
BibTeX
@misc{eprint-2008-17737,
  title={Fast Algorithms for Arithmetic on Elliptic Curves Over Prime Fields},
  booktitle={IACR Eprint archive},
  keywords={public-key cryptography / Elliptic Curve Cryptography},
  url={http://eprint.iacr.org/2008/060},
  note={Thesis, University of Calgary, 2007 nicholas.sullivan@gmail.com 13913 received 3 Feb 2008},
  author={Nicholas T. Sullivan},
  year=2008
}