And Sage also already contains not one but two implementations of Weil pairing (via Tate pairing) written by me, one version within mwrank and the other in gp scripts.
The latter could easily be wrapped into Sage, but has not apparently been done. In the same code there is more useful functionality, namely given a point of order m to construct the function whose divisor is m(P)-m(0). It uses Miller's algorithm. John On 21/11/2007, Robert Bradshaw <[EMAIL PROTECTED]> wrote: > > On Nov 21, 2007, at 1:03 PM, Iftikhar Burhanuddin wrote: > > > On Wed, 21 Nov 2007, Robert Bradshaw wrote: > >> On Nov 21, 2007, at 8:22 AM, William Stein wrote: > >>> On Nov 21, 2007 8:17 AM, Steffen <[EMAIL PROTECTED]> wrote: > >>>> > >>>> Hi, I needed some calculation period benchmark for pairings. I > >>>> could > >>>> not find anything build in, but the following implementation > >>>> solved my > >>>> problem: > >>>> > >>>> http://maths.straylight.co.uk/archives/104 > >> > >> I also implemented the Tate pairing (in SAGE), but it's probably > >> nowhere near as optimized as the one above. (I also didn't verify > >> correctness except that it was indeed a bilinear pairing on curves.) > > > > Hi Robert, > > > > Is your code part of SAGE? I couldn't find it on sage.math. > > No, not yet... I'll get it there though. > > > sage: version() > > 'SAGE Version 2.8.12, Release Date: 2007-11-06' > > > > I presume your implementation is based on Miller's algorithm. The > > implementation at the above link is based on Stange's Elliptic Nets > > algorithm. Pari/GP scripts to compute the Tate Pairings, Elliptic > > Divisibilty Sequences are available on her webpage. > > > > http://www.math.brown.edu/~stange/ > > > > It'll be nice to have both Miller's and Stange's implementations of > > the > > Tate pairing in SAGE. Both algorithms have the same asymptotic time > > complexity (differ in the mutlitplicative constants). > > > > Regards, > > Ifti > > > > > > > > > > -- John Cremona --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
