Create an 'Initial' Private Kernel Circuit

[dbanks12]

Migrated from archived circuits repo: AztecProtocol/aztec3-circuits#200

"""
Currently, there's only 1 private kernel circuit.

That means for the very first iteration, we need to generate dummy 'previous kernel data'. The way we generate this data is inefficient, and the way we generate this data is inefficient (because we're currently generating actual VKs over a mock circuit).

Todo:

• Separate c_bind for calling the initial native previous kernel circuit
• A new struct for InitialPrivateKernelInputs and InitialPrivateKernelPublicInputs
• Remove code which generates a dummy previous kernel (unless needed for testing, but I don't think we'll need that)
• Write an initial native previous kernel circuit, which skips 'previous kernel proof verification' and any 'recursive case' logic
  • Make sure to re-use common codepaths between this circuit and the existing 'recursive' private kernel circuit (refactor to put functions in common files, if needed).
  • Make sure this circuit can only be called in the 'base case' (by including appropriate assertions inside the circuit)
• Update the existing 'recursive' private kernel circuit:
  • remove:
    • The signature verification
    • TxRequest validation (we might even be able to remove the SignedTxRequest input altogether)
    • The 'base case' logic
    • Contract deployment logic (for now)
  • keep:
    • Verification of the 'previous kernel data'
    • recursive case logic
    • etc.
  • new:
    • A check on the previous kernel data's verification key -- that it matches the hard-coded one of the initial kernel circuit, when executing private_call_count = 2. (I.e. we're enforcing that private_call_count = 1 used the 'initial' circuit).
      • Note: for subsequent iterations of the kernel circuit, we can't check the verification key within the kernel circuit, because that's cyclic! We defer such verification key checks to the base rollup circuit. (A separate issue will be opened for this).
• Typescript:
  • Work with someone to make corresponding changes to all the typescript code (mainly in the kernel-prover package), including structs.

"""

Story subtasks:

1. Split private_kernel__sim cbind into ...sim and ...initial_sim #502
2. Create native_private_kernel_initial function #503
3. Move logic between initial and inner private kernels #504
4. Update private_kernel__initial_sim cbind to use underlying initial function #505

[dbanks12]

We'll want to mimic some of what has been done for the public kernel. We can move some logic into a common.hpp. Constructor logic only needs to be in the initial kernel. We may want to consider renaming some public kernel functions and structs if we decide on more intuitive names for their private kernel workalikes.

[dbanks12]

Note after starting work in #549:

1. We'll want to add the CombinedHistoricTreeRoots to the PrivateKernelInputsInitial to initialize public_inputs.constants.
2. We can initialize public_inputs.constants.tx_context from the tx_request.
3. Since we discovered that there were checks missing comparing tx request against private call, we should add test cases that would catch this
4. We shouldn't hesitate to refactor the public kernel to match ours as we move forward with the private kernel split

[iAmMichaelConnor]

Closing, as status moved to 'Done' (it's a GitHub bug)