Re: Reduced Tate pairing in supersingular elliptic curves

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

On Tue, Apr 17, 2018 at 10:10:49PM +0300, Aleksandr Lenin wrote:
> Hi all,
> 
> I have stepped across the case when I get a trivial value 1 for the
> reduced Tate pairing for seemingly legit inputs. Both inputs belong to
> the r-torsion, point 1 is defined over the base-field subgroup, point 2
> does not belong to the base-field subgroup (and it shouldn't, as the
> reduced Tate pairing is supposed to return 1 if two points belong to the
> same subgroup). But the result is nevertheless 1, although in theory it
> looks like it shouldn't.
> 
> I attach the C++ code for libPARI with inputs and the code I was using
> to produce this result.

Hello Aleksandr,

Unfortunately, your code does not compile. Please consider sending GP
code example instead.

My reading is that you are calling FF_elltatepairing with a parameter p1
whose coefficients are t_INT and not t_FFELT.

This is not valid. You need to convert the components of p1 to FFELT or
use the high-level function elltatepairing.

Cheers,
Bill.