A Survey of Interactive Verifiable Computing: Utilizing Low-degree Polynomials

TL;DR

This survey comprehensively reviews the evolution of verifiable computing, emphasizing the role of low-degree polynomials and interactive proof systems in enhancing verification efficiency and soundness.

Contribution

It provides a detailed overview of key protocols and mathematical frameworks, offering both accessible explanations and in-depth analysis for researchers and newcomers.

Findings

Highlights the significance of low-degree polynomials in verification protocols.

Explains the role of protocols like GKR in modern verifiable computing.

Synthesizes historical and recent advancements in the field.

Abstract

This survey provides a comprehensive examination of verifiable computing, tracing its evolution from foundational complexity theory to modern zero-knowledge succinct non-interactive arguments of knowledge (ZK-SNARKs). We explore key developments in interactive proof systems, knowledge complexity, and the application of low-degree polynomials in error detection and verification protocols. The survey delves into essential mathematical frameworks such as the Cook-Levin Theorem, the sum-check protocol, and the GKR protocol, highlighting their roles in enhancing verification efficiency and soundness. By systematically addressing the limitations of traditional NP-based proof systems and then introducing advanced interactive proof mechanisms to overcome them, this work offers an accessible step-by-step introduction for newcomers while providing detailed mathematical analyses for researchers. Ultimately, we synthesize these concepts to elucidate the GKR protocol, which serves as a foundation for contemporary verifiable computing models. This survey not only reviews the historical and theoretical advancements in verifiable computing over the past three decades but also lays the groundwork for understanding recent innovations in the field.