Re: What’s the pari/gp function for the Miller’s algorithm ?

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

On Sun, Mar 15, 2026 at 02:35:26PM +0100, Laël Cellier wrote:
> Le 15/03/2026 à 14:07, Bill Allombert a écrit :
> 
> > On Sun, Mar 15, 2026 at 01:49:37PM +0100, Laël Cellier wrote:
> > > Bonjour,
> > > in Sagemath, it s being exposed as _miller_() but what the Pari/gp
> > > equivalent ? This would be for implementing the attachment below where the
> > > Miller output is completely bilinear directly without divisions or final
> > > exponentiation.
> > You can simply use elltatepairing since it does not do the final exponentiation.
> > 
> > Cheers,
> > Bill.
> 
> Hi, but then this doesn’t seems to be tunable for the papers attached which
> is a ate pairing (the case where no division or final exponentiation is
> required after the Miller step)… Or am I getting it wrong ?

The thig is, PARI elltatepairing actually computes the ate pairing.

Cheers,
Bill