We present a geometric interpretation of the group law on Jacobi quartic curves, %and our formulae for Miller's %algorithm come from this interpretation. which leads to formulae for Miller's algorithm. The doubling step formula is competitive with that for Weierstrass curves and Edwards curves. Moreover, by carefully choosing the coefficients, there exist quartic twists of Jacobi quartic curves from which pairing computation can benefit a lot. Finally, we provide some examples of supersingular and ordinary pairing friendly Jacobi quartic curves.
Category / Keywords: public-key cryptography / elliptic curve, pairing, geometric interpretation Publication Info: unpublished Date: received 6 Sep 2010, last revised 25 Oct 2010 Contact author: hwang at is ac cn Available format(s): PDF | BibTeX Citation Version: 20101025:075258 (All versions of this report) Short URL: ia.cr/2010/475 Discussion forum: Show discussion | Start new discussion