[curves] Curve cycles

[Watson Ladd]

But now there is a number theory problem: prove the examples we have are it
or find more.

And I don't believe this has been approched.

On Sat, Aug 18, 2018 at 5:10 AM Michael Scott <mike.scott at miracl.com> wrote:
>
> I really don't expect any other cycles to be found, outside the simple
MNT case. The search for pairing-friendly curves is I suspect largely
complete at this stage.
>
> Mike Scott
>
> On Sat, Aug 18, 2018 at 1:29 PM Jeff Burdges <burdges at gnunet.org> wrote:
>>
>>
>> Is anyone actively working on cycles of pairing friendly elliptic curves?
>>
>> In other words, each curve’s field of definition is the scalar field of
it’s predecessor, which makes recursive composition of SNARKs not totally
insane:
>> https://www.iacr.org/archive/crypto2014/86160202/86160202.pdf
>>
>> I’d think you’d want to explore a lot of possible optimisations beyond
that paper before trying to use something like this, so maybe someone has
tried?
>>
>> In practice, I’m unsure if recursively composed SNARKs really give you
much since, if you want to add a SNARK layer, then you still need access to
some large database, but.. that discussion might veer off topic for here.
>>
>> Best,
>> Jeff
>>
>> p.s.  We’re hiring cryptographers at the web 3 foundation :
https://web3.foundation/jobs
>>
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>
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