[BASE] Anemoi hash r1cs

[vesselinux]

Related to Issue #54. See also https://eprint.iacr.org/2022/840 for details.
This PR and branch are the destination for future anemoi-related changes.

[dtebbs]

This PR includes all the plonk changes, so it's almost impossible to review.
Could you poinit it at the relevant branch so I can take a look at this.

[vesselinux]

This PR includes all the plonk changes, so it's almost impossible to review. Could you poinit it at the relevant branch so I can take a look at this.

Done. This branch now points to plonk which is the correct branch it is based on. Sorry!

[dtebbs]

Good firs attempt. You've got the constraints being formed correctly. I think there are a couple of optimizations to do here, and these simple examples are great to use to discuss that. Also some intermediate values can potentially be removed.

Let's discuss this on a call.

[dtebbs]

Yes, functionally this looks correct. I think we can improve the clarity a bit.

[dtebbs]

Suggestion for how to reuse the gadget

class anemoi_power_two_round_1_gadget : public anemoi_power_two_gadget
{
anemoi_power_two_round_1_gadget(
rotoboard<FieldT> &pb,
        const pb_variable<FieldT> &input,
        const pb_variable<FieldT> &output,
        const std::string &annotation_prefix = "")
  : anemoi_power_two_gadget(..., ...ALPHA, ... BETA, ...)
  {
  }
}

class anemoi_power_two_round_2_gadget : public anemoi_power_two_gadget
{
anemoi_power_two_round_2_gadget(
rotoboard<FieldT> &pb,
        const pb_variable<FieldT> &input,
        const pb_variable<FieldT> &output,
        const std::string &annotation_prefix = "")
  : anemoi_power_two_gadget(..., anemoi_constants_selector<ppT>::BETA, ... anemoi_constants_selector<ppT>::GAMMA, ...)
  {
  }
}

[dtebbs]

Quick intermediate review.