Computing the Weil-Pairing over Elliptic Curves in SAGE

[Spit]

Hi all,

I have a little problem in which the documentation, google etc can't
help me.

Is there any possibility to compute the Weil-Pairing over Ellitic
Curves in Sage like it is possible in Magma for example?

The only thing I found was a little written skript which is not very
helpful in my case.

Benedikt

[John Cremona]

Dear Benedikt,

There is code to compute the Weil pairing using a gp script (written
by me) which sage includes, but at present there is no wrapper for it
to be used in Sage. Either that could be done, or someone could
rewrite that gp script in Sage.

John Cremona

--
John Cremona

[Martin Albrecht]

Hi there,

let me (ab)use this opportunity to point to a library for doing these things
over finite fields (for crypto) I came across by chance.

http://crypto.stanford.edu/pbc/

PBC stands for Pairing-Based Cryptography and is a library for ... well ...
pairings in cryptography (where everybody is pretty crazy about pairings
these days). The focus seems to be 'industrial' applications rather than
research (playing around).

It is
* GPL v3 (!)
* well documented: reference manual, tutorial, examples
* small: 500k
* used by a couple of applications
* claimed to be fast: I have no idea how fast 'fast' should be though

So if you care about pairings, it might be worth a look/wrap etc.

Cheers,
Martin

PS: The PBC website links to Sage btw.

--
name: Martin Albrecht
_pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99
_www: http://www.informatik.uni-bremen.de/~malb
_jab: martinr...@jabber.ccc.de

[John Cremona]

Sounds like a good idea, and certainly vastly better than my gp code
which was really only a toy.

I CC'ed this so sge-devel.

John

--
John Cremona