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

Le 15/03/2026 =C3=A0 14:44, Bill Allombert a =C3=A9crit=C2=A0:

> On Sun, Mar 15, 2026 at 02:35:26PM +0100, La=C3=ABl Cellier wrote:
>> Le 15/03/2026 =C3=A0 14:07, Bill Allombert a =C3=A9crit=C2=A0:
>>
>>> On Sun, Mar 15, 2026 at 01:49:37PM +0100, La=C3=ABl Cellier wrote:
>>>> Bonjour,
>>>> in Sagemath, it s being exposed as _miller_() but what the Pari/gp
>>>> equivalent=E2=80=AF?=C2=A0This would be for implementing the attachm=
ent below where the
>>>> Miller output is completely bilinear directly without divisions or f=
inal
>>>> exponentiation.
>>> You can simply use elltatepairing since it does not do the final expo=
nentiation.
>>>
>>> Cheers,
>>> Bill.
>> Hi, but then this doesn=E2=80=99t seems to be tunable for the papers a=
ttached which
>> is a ate pairing (the case where no division or final exponentiation i=
s
>> required after the Miller step)=E2=80=A6 Or am I getting it wrong=E2=80=
=AF?
> The thig is, PARI elltatepairing actually computes the ate pairing.
>
> Cheers,
> Bill

Are you sure=E2=80=AF? The scientific publication attached=20
https://www.researchgate.net/profile/Florian-Hess-2/publication/221348700=
_Ate_Pairing_on_Hyperelliptic_Curves/links/0c96051dbc7c0a3178000000/Ate-P=
airing-on-Hyperelliptic-Curves.pdf=20
seems to describe a specific way to use the Miller algorithm in order to=20
create their variant of the ate pairing=E2=80=A6

Or at least I don=E2=80=99t understand the paper in the way that just sel=
ecting=20
the right elliptic curve will lead to the ate pairing being bilinear=20
without a coset.

Cordialement,