Create a Stark prover and verifier from zero, with Rust. Hopefully without external libraries.

The point is to create a minimal version without strong security requirements or optimizations.

Implement a very simple hashing algorithm.

Implement at least addition, subtraction and multiplication. Possibly division.

Craft an execution trace to prove, as input for the prover.

Implement FRI logic. This requires at least:

Implement evaluating polynomials.

Implement.

Implement polynomial interpolation.

Possibly we can get by without an extension field, at least for the first version.