This report describes the state of the art in verifiable computation. The problem being solved is the following: The Verifiable Computation Problem (Verifiable Computing Problem) Suppose we have two computing agents. The first agent is the verifier, and the second agent is the prover. The verifier wants the prover to perform a computation. The verifier sends a description of the computation to the prover. Once the prover has completed the task, the prover returns the output to the verifier. The output will contain proof. The verifier can use this proof to check if the prover computed the output correctly. The check is not required to verify the algorithm used in the computation. Instead, it is a check that the prover computed the output using the computation specified by the verifier. The effort required for the check should be much less than that required to perform the computation. This state-of-the-art report surveys 128 papers from the literature comprising more than 4,000 pages. Other papers and books were surveyed but were omitted. The papers surveyed were overwhelmingly mathematical. We have summarised the major concepts that form the foundations for verifiable computation. The report contains two main sections. The first, larger section covers the theoretical foundations for probabilistically checkable and zero-knowledge proofs. The second section contains a description of the current practice in verifiable computation. Two further reports will cover (i) military applications of verifiable computation and (ii) a collection of technical demonstrators. The first of these is intended to be read by those who want to know what applications are enabled by the current state of the art in verifiable computation. The second is for those who want to see practical tools and conduct experiments themselves.

翻译：本报告概述了可验证计算领域的最新进展。所解决的问题如下：可验证计算问题（可验证计算问题）假设存在两个计算主体。第一个主体为验证者，第二个主体为证明者。验证者希望证明者执行特定计算任务。验证者向证明者发送计算描述。证明者完成任务后，将输出结果返回给验证者，该输出结果包含证明信息。验证者可利用此证明检验证明者是否正确计算结果。此检验无需验证计算过程中使用的算法，而是验证证明者是否按照验证者指定的计算方式生成输出结果。检验所需工作量应远小于执行原始计算所需工作量。本进展报告调研了文献中128篇论文（合计超过4000页），另涉及其他被调研但未纳入的论文与书籍。所调研论文以数学类居多。我们归纳了构成可验证计算基础的核心理念。报告包含两大章节：首章（篇幅较大）阐述概率可检验证明与零知识证明的理论基础；第二章描述可验证计算的当前实践。后续两份报告将分别涵盖：（i）可验证计算的军事应用，（ii）技术演示案例合集。前者旨在帮助读者了解当前可验证计算技术所支持的应用场景，后者为希望接触实用工具并开展实验的读者提供参考。