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Paper: Fast Point Multiplication on Elliptic Curves of Even Order

Authors:
Rongquan Feng
Hongfeng Wu
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URL: http://eprint.iacr.org/2007/377
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Abstract: Every elliptic curve of even order over a finite field of characteristic >3 is birationally equivalent to a curve in Jacobi quartic form. This paper presents the fast explicit formulas for group operations on a Jacobi quartic curve. The algorithm for doubling uses only 1M+6S, for the mixed-addition uses only 8M+2S and the unified addition formula only 9M+2S to be the best case. For elliptic curve of even order, these algorithm are more efficient than the other algorithms in the literature.
BibTeX
@misc{eprint-2007-13657,
  title={Fast Point Multiplication on Elliptic Curves of Even Order},
  booktitle={IACR Eprint archive},
  keywords={foundations / Elliptic curve, Point Multiplication, Jacobi quartic, Unified Formula,Side-Channel Analysis},
  url={http://eprint.iacr.org/2007/377},
  note={ wuhfmail@gmail.com 13794 received 23 Sep 2007, last revised 4 Oct 2007, withdrawn 8 Oct 2007},
  author={Rongquan Feng and Hongfeng Wu},
  year=2007
}