ZK-SNARK
Also: Zero-knowledge proof · STARK
A proof that a computation was performed correctly, short enough to check quickly and revealing nothing about the inputs beyond the truth of the statement.
The verifier learns one thing: that the claim holds. Not the inputs, not the intermediate steps. The proof is small and cheap to check regardless of how large the original computation was, which is what makes it useful for settlement — a chain can verify work it never performed.
Hash-based systems and what they rest on
Hash-based constructions underpin zkrollups, zkVMs and post-quantum roadmaps. Their security rests on Reed-Solomon proximity gaps, and there is a gap between what these systems are assumed to guarantee and what has been formally proved about them. That gap is an active research target, with machine-checked bounds being pushed upward against benchmarks a proof assistant adjudicates.
The practical caveat when comparing systems
Papers in this area report asymptotics far more often than timings on shared hardware. The question worth asking of a proving stack is not which claims the better complexity but which has been measured against the others on the same machine.