Re: miller functions for elliptic curves

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

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.