Remote Computation Verification With Low-Overhead Succinct Arguments
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing interactive proof systems incur significant overhead for the prover, making them inefficient for widespread deployment, particularly in verifying computational statements, and there is a need for succinct arguments with negligible soundness error and reduced prover complexity.
Innovation Solution
Construct succinct arguments and interactive oracle proofs for Boolean circuits with 2−λ soundness error and polylog(λ) prover overhead using linear-size computable hash functions and specific matrix representations, along with efficient error reduction techniques for multi-sumcheck protocols.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If succinct arguments with constant soundness error are constructed using linear-size provers, then prover overhead is reduced to linear size, but soundness error remains constant rather than negligible
Solution Approach 1:
The protocol segments the verification process into multiple independent rounds, each contributing a constant factor to soundness reduction. By composing O(λ) such rounds, the overall soundness error becomes 2^(-λ), transforming constant soundness into negligible soundness while maintaining linear prover overhead through efficient composition techniques.
Solution Approach 2:
The protocol employs periodic repetition of the base argument system O(λ) times, where each repetition independently contributes to soundness reduction. This periodic execution structure allows the prover to maintain linear overhead while the cumulative effect of multiple rounds achieves negligible soundness error.
2Reliability
If straightforward repetition is used to reduce soundness error, then soundness becomes negligible, but prover overhead increases multiplicatively to O(S·λ)
Solution Approach 1:
The protocol merges multiple argument instances into a single composed protocol where the prover processes all instances in parallel rather than sequentially. This combining approach reduces the multiplicative overhead O(S·λ) to a more efficient complexity by sharing common computational components across all O(λ) repetitions.
Solution Approach 2:
The base argument system is designed as a universal building block that can be efficiently replicated and composed multiple times. The prover implements a multi-functional routine that handles O(λ) instances using the same core logic, avoiding the need for separate processing for each instance and thus reducing overhead from O(S·λ) to near-linear complexity.
3Reliability
If working over 2λ-size finite fields is used to achieve negligible soundness error, then soundness becomes 2^(-λ), but prover overhead increases to O(S·λ)
Solution Approach 1:
The protocol changes the parameter regime by working over smaller λ-size fields rather than 2λ-size fields, combined with O(λ) repetitions. This parameter transformation achieves the same negligible soundness error 2^(-λ) while reducing prover overhead from O(S·λ) to O(S·polylog(λ)) by exploiting the efficiency of smaller field operations.
Data Source
AI summary
A method and apparatus for efficient protocols for verifying remote computations, with particular application for cloud-based services and mobile environments are disclosed. The protocols utilize succinct arguments that rely on the existence of subexponentially secure linear-size computable collision-resistant hash functions. The class of Boolean circuits that can be handled includes circuits with a repeated sub-structure, which arise in natural applications such as batch computation/verification, hashing, and related block chain applications.