Simple M31 AIR Example

This chapter presents a complete example of implementing a simple AIR over the Mersenne31 field.

Problem Description

We'll implement an AIR that proves knowledge of a sequence where each element is the square of the previous element.

Implementation

Step-by-Step Explanation

1. Column Definition: Single column for the sequence values
2. Transition Constraint: Each value is the square of the previous
3. Boundary Constraint: Sets the initial value
4. Proving: Generates a proof of the sequence
5. Verification: Checks the proof's validity