Time-Optimal Interactive Proofs for Circuit Evaluation

Abstract

Abstract. Several research teams have recently been working toward the development of practical general-purpose protocols for verifiable computation. These protocols enable a computationally weak verifier to offload computations to a powerful but untrusted prover, while providing the verifier with a guarantee that the prover performed the requested computations correctly. Despite substantial progress, existing implementations require further improvements before they become practical for most settings. The main bottleneck is typically the extra effort required by the prover to return an answer with a guarantee of correctness, compared to returning an answer with no guarantee.We describe a refinement of a powerful interactive proof protocol due to Goldwasser, Kalai, and Rothblum [20]. Cormode, Mitzenmacher, and Thaler [14] show how to implement the prover in this protocol in time O(S log S), where S is the size of an arithmetic circuit computing the function of interest. Our refinements apply to circuits with sufficiently "regular" wiring patterns; for these circuits, we bring the runtime of the prover down to O(S). That is, our prover can evaluate the circuit with a guarantee of correctness, with only a constant-factor blowup in work compared to evaluating the circuit with no guarantee.We argue that our refinements capture a large class of circuits, and we complement our theoretical results with experiments on problems such as matrix multiplication and determining the number of distinct elements in a data stream. Experimentally, our refinements yield a 200x speedup for the prover over the implementation of Cormode et al., and our prover is less than 10x slower than a C++ program that simply evaluates the circuit. Along the way, we describe a specialpurpose protocol for matrix multiplication that is of interest in its own right.Our final contribution is the design of an interactive proof protocol targeted at general data parallel computation. Compared to prior work, this protocol can more efficiently verify complicated computations as long as that computation is applied independently to many different pieces of data.

Efficiently Verifiable Computation on Encrypted Data

“…Yet another approach used FHE as a tool to build efficient verification of arbitrary computations [26,2,23]. Several implementational efforts [24,54,55,59,49,11,60] show that also in this area we are on the verge of achieving practical efficiency, with the quadratic span program techniques of [27,49] showing particular promise.…”

Primitives towards verifiable computation: a survey

“…In Ref. [115], Thaler worked out on large classes of circuits with regular wiring patterns, and reduced down the linearithmic factor of Ref. [55] up to linear.…”

Engineering a Delegatable and Error-Tolerant Algorithm for Counting Small Subgraphs

“…Cormode, Mitzenmacher, and Thaler [38] and Thaler [105]) and recent theoretical work in the context of fine-grained complexity (see above) suggest that in the context of specific problems and algorithm designs one could make an engineering push towards increasingly practical and non-interactive delegation on extensive infrastructure. This paper seeks to make such a demonstration together with an open-source release [71] to ease further practical developments.…”

“…(Cf. also Cormode, Mitzenmacher, and Thaler [38], and Thaler [105] for problem-specific work.) Continuing on the ideas of Williams, the objective of pushing univariate proof systems towards algorithm designs meeting the simultaneous goals of parallelizability, error-tolerance, and matching in total complexity the best known algorithms for specific problems is explored by Björklund and Kaski [27].…”