Re: miller functions for elliptic curves

[Pierre Charollois <pierre.charollois@gmail.com>]

I need a function with  divisor m[P] - m[OE], for an elliptic curve over Q, and P, Q  arbitrary torsion points.

I can probably code this naively myself, but maybe there are for instance tricks that reduce the number of iterations. (I noticed papers about this).

Cheers,

Pierre

Le ven. 4 févr. 2022 à 17:04, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> a écrit :

On Fri, Feb 04, 2022 at 04:20:53PM +0100, Pierre Charollois wrote:
> Hello,
>
> in the documentation for elliptic curves, a Miller functions f_{m, P} seems
> to be
> coded for curves over finite fields
>
> " More precisely, let fm,P denote a Miller function with divisor m[P] - m[OE];
> the algorithm returns fm,P(Q) ∈ k*/(k*)^m.".
>
> I am curious about the code for this function fm, P.
> Is it available for any field, not only finite fields ?

It is available only for finite fields and only in evaluated form,
as above. It is essentially identical to elltatepairing.

I have a more general GP implementation.
What do you need ?

Cheers,
Bill.