GKR extended to approximate interactive proofs over complex circuits
Original title: Delegating Computation with Approximate Arithmetic: Interactive Proofs for Wizards
At constant soundness the verifier runs in (n+1) poly(L, log S, b); the honest prover needs O(S log S) complex operations.
The paper gives public-coin interactive proofs for logspace-uniform layered arithmetic circuits over the complex numbers in which both prover and verifier compute approximately. A claimed output must be close to the exact circuit output under public bounds on gate values and wiring coefficients. The construction also yields zero-knowledge proofs from one-way functions, one-round arguments from private information retrieval, and interactive PCPs polynomial in the witness length.
Unconfirmed: The claim of being first is the authors' assessment.
- Communication is poly(L, log S, b) and prover time is poly(S, b).
- Gates are labeled by complex roots of unity rather than a random line.
- Error thresholds are chosen backward from the input layer.
- Authors call these the first doubly efficient approximate interactive proofs.
From the original article
1 min read at arxiv.orgWe study interactive proofs for arithmetic circuits over the complex numbers $\mathbb{C}$ in which both the prover and the verifier compute approximately (unlike muggles, wizards can use magic, i. e. , floating-point numbers).
By Aritra Das · arxiv.org
A short excerpt; the article and its images belong to the publisher. Summary, key facts and assessment above are AI-written from the article and can be wrong.