[Discussion] Arrabbiata: IVC witness for first instance

[dannywillems]

While generating incrementally a proof, how the base case is handled is often a discussion. This issue will gather different ideas, with their pros/cons:

Using dummy values with a fixed IVC circuit size

The circuit for the whole computation (noted F') can contain a fixed part to handle the verifier part (i.e. so-called the IVC circuit).
The first witness will therefore contain "dummy satisfying values", and the accumulation would work as for the next iterations.

Pros:

• no additional constraints
• no "selection" at "runtime" (understand "runtime" in this case as the witness computation).

Cons:

• Must be carefully crafted.
• if the IVC circuit is huge, for small incremental computation, the overhead can be non-negligible.

Using a selector

The verifier can be "deactivated" on the first run, and the actual application (noted F), can have more space in the first witness.

Pros:

• Small incremental computation benefits from it

Cons:

• requires additional constraints.
• might require to increase the degree of the constraints.