On a new generalization of Huff curves

Abdoul Aziz Ciss; Djiby Sow

Paper 2011/580

On a new generalization of Huff curves

Abdoul Aziz Ciss and Djiby Sow

Abstract

Recently two kinds of Huff curves were introduced as elliptic curves models and their arithmetic was studied. It was also shown that they are suitable for cryptographic use such as Montgomery curves or Koblitz curves (in Weierstrass form) and Edwards curves. In this work, we introduce the new generalized Huff curves $a x (y^{2} - c) = b y (x^{2} - d)$ with $a b c d (a^{2} c - b^{2} d) \neq 0$ , which contains the generalized Huff's model $a x (y^{2} - d) = b y (x^{2} - d)$ with $a b d (a^{2} - b^{2}) \neq 0$ of Joye-Tibouchi-Vergnaud and the generalized Huff curves $x (a y^{2} - 1) = y (b x^{2} - 1)$ with $a b (a - b) \neq 0$ of Wu-Feng as a special case. The addition law in projective coordinates is as fast as in the previous particular cases. More generally all good properties of the previous particular Huff curves, including completeness and independence of two of the four curve parameters, extend to the new generalized Huff curves. We verified that the method of Joye-Tibouchi-Vergnaud for computing of pairings can be generalized over the new curve.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Huff curves pairing divisor Jacobian Miller algorithm elliptic curve models Edwards curves Koblitz Curves
Contact author(s): abdoul ciss @ ucad edu sn
History: 2011-11-02: received
Short URL: https://ia.cr/2011/580
License: CC BY

BibTeX

@misc{cryptoeprint:2011/580,
      author = {Abdoul Aziz Ciss and Djiby Sow},
      title = {On a new generalization of Huff curves},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/580},
      year = {2011},
      url = {https://eprint.iacr.org/2011/580}
}