Proofs of correct computation built only from hash functions: no secret setup, likely quantum-safe, but bigger.
The idea: The computation's steps are written into a big table, and the table is turned into polynomials that only behave nicely if every step was right. The prover commits to them with Merkle trees, and the verifier asks to see a few random spots. Cheating anywhere would make the polynomials badly irregular, so random spot checks catch it with overwhelming probability. Hashing the commitments replaces the verifier's random questions (Fiat-Shamir), so the proof is just a file that anyone can check.
Why it matters: Used by some blockchain scaling systems.
On the map: FRI: transparent, no setup
Proofs of correct computation built only from hash functions[1]: transparent (no trusted setup) and plausibly secure against quantum computers, at the cost of larger proofs, tens to hundreds of KB.
They rely on collision-resistant hashing (Merkle trees), on Fiat-Shamir with a real hash (the FS tag, proven only in the random oracle model)[2] and, for many parameter choices, a still-unproven form of the proximity-gap conjectures (the strongest form was disproved in 2025). As with every succinct argument, an idealized model is unavoidable (Gentry-Wichs)[3]. Used by zkVMs and rollups.
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.