Re: Reduced Tate pairing in supersingular elliptic curves

[Aleksandr Lenin <aleksandr.lenin@cyber.ee>]

In this particular case, the two point do not necessarily belong to the
t-torsion. Nevertheless, the pairing should be non-trivial, as shown in
the random pairing example, where a reduced pairing between p1 and a
random point on an elliptic curve produces non-trivial result, but with
the inputs I am using the result is 1.

On 04/17/2018 10:10 PM, 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.
> 
> I would be grateful for any advice on why could this happen, possible
> fixes, and possible ways to optimize this code a bit so that it would
> work faster (I know the code is ugly, I am a beginner PARI user).
> 
> Thanks in advance,
> 

-- 
With kind regards,

Aleksandr Lenin
Researcher
Information Security Research Institute
Cybernetica AS
Mäealuse 2/1, 12618 Tallinn, ESTONIA
www.cybernetica.eu