交互式可验证计算综述：利用低次多项式
A Survey of Interactive Verifiable Computing: Utilizing Low-degree Polynomials
AI总结：
本文综述可验证计算从复杂性理论到 ZK-SNARKs 的发展，重点梳理低次多项式、sum-check 与 GKR 协议等交互式证明技术及其理论基础。
摘要：
本综述对可验证计算进行了全面考察，追溯其从基础复杂性理论到现代零知识简洁非交互式知识论证（ZK-SNARKs）的演进。我们探讨了交互式证明系统、知识复杂性以及低次多项式在错误检测和验证协议中的应用等关键发展。本综述深入研究了 Cook-Levin 定理、sum-check 协议和 GKR 协议等基本数学框架，强调它们在提升验证效率和可靠性方面的作用。通过系统地分析传统基于 NP 的证明系统的局限性，并随后引入先进的交互式证明机制来克服这些局限，本工作为新手提供了易于理解的循序渐进介绍，同时为研究人员提供了详细的数学分析。最终，我们综合这些概念来阐明 GKR 协议，该协议是当代可验证计算模型的基础。本综述不仅回顾了过去三十年间可验证计算在历史和理论上的进展，也为理解该领域近期的创新奠定了基础。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
