<div dir="auto">But now there is a number theory problem: prove the examples we have are it or find more.<div dir="auto"> </div><div dir="auto">And I don't believe this has been approched.</div></div> On Sat, Aug 18, 2018 at 5:10 AM Michael Scott <<a href="mailto:mike.scott@miracl.com" target="_blank" rel="noreferrer">mike.scott@miracl.com</a>> 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 <<a href="mailto:burdges@gnunet.org" target="_blank" rel="noreferrer">burdges@gnunet.org</a>> 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: >> <a href="https://www.iacr.org/archive/crypto2014/86160202/86160202.pdf" rel="noreferrer noreferrer" target="_blank">https://www.iacr.org/archive/crypto2014/86160202/86160202.pdf</a> >> >> 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 : <a href="https://web3.foundation/jobs" rel="noreferrer noreferrer" target="_blank">https://web3.foundation/jobs</a> >> >> _______________________________________________ >> Curves mailing list >> <a href="mailto:Curves@moderncrypto.org" target="_blank" rel="noreferrer">Curves@moderncrypto.org</a> >> <a href="https://moderncrypto.org/mailman/listinfo/curves" rel="noreferrer noreferrer" target="_blank">https://moderncrypto.org/mailman/listinfo/curves</a> > > _______________________________________________ > Curves mailing list > <a href="mailto:Curves@moderncrypto.org" target="_blank" rel="noreferrer">Curves@moderncrypto.org</a> > <a href="https://moderncrypto.org/mailman/listinfo/curves" rel="noreferrer noreferrer" target="_blank">https://moderncrypto.org/mailman/listinfo/curves</a>