This is about the point where my math and libsnark knowledge runs out :) My usecase is specifically cryptocurrency related, so I'm mostly interested in curves that are used by cryptocurrency signature algorithms. E.g. secp256k1 (Bitcoin and its kids), ed25519 (Sia, Stellar, and a few others). Jubjub is definitely on the list once sapling is closer to deployment. After a bit of consideration, ed25519 would probably be the most interesting at first.

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On Wed, Jan 3, 2018 at 2:33 PM Sean Bowe <s...@z.cash> wrote: > I believe those gadgets are specifically for curves where the scalar > field is the base field of the curve you're working with, so they > probably wouldn't be that useful for arbitrary fields. Most of the > complexity here is the bignum arithmetic inside the circuit, though. > > > Is there any more clever way to do this than just providing splitting > into bits to implement modular arithmetic in a different field? > > Not that I know of. I explored the feasibility of this kind of stuff > in the past and concluded each point addition would be around the cost > of a SHA256 invocation. You can minimize the number of additions using > window tables. The best approach seemed to be giant window tables > queried with merkle tree lookups using something like MiMC. The > additions are most efficient when working with affine formulas > (inversions can be witnessed as efficiently as multiplications). You > may be able to get this down to 2^20 constraints for ~256-bit scalars, > which might be around 10-20 second proving time. > > Sean > > On Wed, Jan 3, 2018 at 1:36 PM, Andrew Miller <soc1...@illinois.edu> > wrote: > > Suppose one did want to build a secp256k1 gadget. I notice that libsnark > > already provides a general gadget for weierstrass form elliptic curves, > > parameterized by a field. So all we'd have to do is define the secp256k1 > > operations in the alt_bn128 or in bls12 fields. Is there any more clever > way > > to do this than just providing splitting into bits to implement modular > > arithmetic in a different field? > > > > On Jan 3, 2018 2:11 PM, "Sean Bowe" <s...@z.cash> wrote: > >> > >> If any curve is acceptable, I would encourage Jubjub, which we'll be > >> using for the next version of Zcash. In which case you will be able to > >> leverage our Sapling crypto code once it is more mature over the next > >> month or so. https://github.com/zcash-hackworks/sapling-crypto > >> > >> Sean > >> > >> On Wed, Jan 3, 2018 at 1:02 PM, James Prestwich via zapps-wg > >> <zapps...@lists.z.cash.foundation> wrote: > >> > I'd prefer sha256 or bitcoin-style hash160. I'm interested in a few > >> > different curves, including secp256k1. Eventually for EdDSA keys as > >> > well. Is > >> > there a list of supported curve operations? > >> > > >> > On Wed, Jan 3, 2018 at 12:57 PM Andrew Miller <soc1...@illinois.edu> > >> > wrote: > >> >> > >> >> Thank you so much for expressing your question in Camenisch-Stadler > >> >> notation! That makes it very clear what you're going for. > >> >> > >> >> What hash function H do you have in mind, would SHA2 work? Also what > >> >> group > >> >> G do you have in mind, secp256k1? > >> >> > >> >> If so, I do not know of any existing implementation of secp256k1 > >> >> operations specifically in libsnark, so that would presumably be the > >> >> biggest > >> >> challenge. > >> >> > >> >> > >> >> On Jan 3, 2018 1:47 PM, "James Prestwich via zapps-wg" > >> >> <zapps...@lists.z.cash.foundation> wrote: > >> >> > >> >> I'd like to participate in the setup ceremony. > >> >> > >> >> I also have an app I'd like to build using a zk-proof of knowledge of > >> >> an > >> >> ECC private key. {(a) : A = a * G, B = H(a)}. Can anyone point me to > >> >> good > >> >> resources on getting started? > >> >> > >> >> > >> > >