I agree John. It could be really cool and intuitive if the pairing also was accessible from the curve group E(F) with the whole torsion of m in it.
In this way points P,Q would intuitively be expected to come from E (F). Wow.. Magma have a lot of pairings implemented.. Think I got my answer, thanks guys! By the way.. Do not know if anyone is interested in flinging some critique my way, I have posted my small Sage implementation of the Weil pairing and BLS short signature scheme here under "files": http://mollerhansen.com /David On 15 Nov., 14:00, "John Cremona" <[EMAIL PROTECTED]> wrote: > 2008/11/15 Martin Albrecht <[EMAIL PROTECTED]>: > > > > > > > On Saturday 15 November 2008, David Møller Hansen wrote: > >> The pairing is 'just' a bilinear mapping of two point in a curve group > >> into a "third" group, type depending on what pairing. > > >> I'm wondering where pairings should go in Sage structure? > > >> - any comments on that? > > > WWMD (What Would Magma Do) ;-) > > >http://magma.maths.usyd.edu.au/magma/htmlhelp/text1285.htm > > > so how about: > > > sage: E = EllipticCurve(...) > > sage: P = E.random_element() > > sage: Q = E.random_element() > > sage: _ = P.tate_pairing(Q,n) > > > I don't work with these objects, so this might be the least desirable > > solution. > > That is the sort of thing I would do, but my use of pairings is not > necessarily similar to those using them in crypto. I would also > expect E.*_pairing(P,Q,n) to work, and for n to be optional with a > sensible default (depending on which pairing), say the order of P. So > if P and Q are both in E[m] then E.weil_pairing(P,Q) and need not > mention m. > > John > > > > > Cheers, > > Martin > > > -- > > name: Martin Albrecht > > _pgp:http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 > > _www:http://www.informatik.uni-bremen.de/~malb > > _jab: [EMAIL PROTECTED] --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
