Performance benchmark of bw6_767

[alv-around]

I am researching on the field of 2-Pairing SNARKs. It has come.
From my understanding any bls12 curve has a matching bw6 curve for that allows for composing.
On the gnark docks, it is stated that the bls12_381 can not be efficiently paired.
I was wondering how inefficient they are compared to efficient curves such as bls12_377/bw6_761.
I noticed that there were some developments on on the bw6_767 on this repo.
So I was wondering if you could provide some valuable insight on the topic.
Specially, since bls12_381 seems to be the most accepted pairing-curve atm (Eth2.0, Algorand, Tezos etc..), so any kind of benchmark would be very useful :)

Looking forward your valuable insight,
thanks in advance!

[yelhousni]

Hi @alvaro-alonso, sorry I haven't seen your question before. Indeed any BLS12 has a matching BW6, but also any BLS24 and BN as we generalised this construction in this paper (see section 5.2 and appendix C). However, in order for the BW6 to be efficient for SNARKs, its subgroup order r should be highly 2-adic i.e. 2^L | r-1 for a big integer L. This means, in the context of 2-chains, that the BLS12 (or BLS24 or BN) should be defined over a field of size p (=r) highly 2-adic. This is the case for BLS12-377 as 2^46 | p-1 but not for BLS12-381 as only 2^1 | p -1.

[alv-around]

@yelhousni thanks for the response :) I was aware of the highly 2-adic r, but your comparison of the value p gives me a better idea of the magnitudes. 🙏