In this work, we introduce the new generalized Huff curves $ax(y^{2} -c) = by(x^{2}-d)$ with $abcd(a^{2}c-b^{2}d)\neq 0$, which contains the generalized Huff's model $ax(y^{2}- d) = by(x^{2}-d)$ with $abd(a^{2}-b^{2})\neq 0$ of Joye-Tibouchi-Vergnaud and the generalized Huff curves $x(ay^{2} -1) =y(bx^{2}-1)$ with $ab(a-b)\neq 0$ 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.
Category / Keywords: public-key cryptography / Huff curves, pairing, divisor, Jacobian, Miller algorithm, elliptic curve models, Edwards curves, Koblitz Curves Date: received 26 Oct 2011 Contact author: abdoul ciss at ucad edu sn Available formats: PDF | BibTeX Citation Version: 20111102:204355 (All versions of this report) Discussion forum: Show discussion | Start new discussion