Add poseidon permutation opcode

[kevaundray]

Problem

Poseidon is a popular circuit friendly hash function, currently we do not have an efficient blackbox function for it like keccak, sha256 and blake.

Happy Case

Add the poseidon permutation opcode

Alternatives Considered

No response

Additional Context

It would be great if we could make the opcode agnostic to the t parameter, this does not seem possible and barretenberg uses a non-standard t parameter for efficiency.

Would be good to investigate whether we can add a more fine grained opcode without losing efficiency and still being agnostic to t

Would you like to submit a PR for this Issue?

No

Support Needs

No response

[guipublic]

I don't see how we could be agnostic to t, unless we hide the state. But I think that if we want to do anything useful with the permutation, we would need to manipulate the state in Noir.
So I believe the opcode should expose the state, and this means its size t as well.

[TomAFrench]

@guipublic Do we really gain much on having the poseidon2 permutation added as a blackbox function rather than in Noir directly? As it's just arithmetic it seems like we'd get all the same benefits from AztecProtocol/aztec-packages#5374?

[guipublic]

I think there is some gain as the gates are tailored to the specific Poseidon operations, i.e they are hand-made crafted as opposed to automatically generated in Noir.
Another point is that using a Honk backend will greatly benefit from the blackbox function, and I think having a Honk backend for Noir is something that we want.

n.b: the poseidon2 permutation is already added as a blackbox.