Streaming interactive proofs (SIPs) enable a space-bounded algorithm with one-pass access to a massive stream of data to verify a computation that requires large space, by communicating with a powerful but untrusted prover. This work initiates the study of zero-knowledge proofs for data streams. We define the notion of zero-knowledge in the streaming setting and construct zero-knowledge SIPs for the two main algorithmic building blocks in the streaming interactive proofs literature: the sumcheck and polynomial evaluation protocols. To the best of our knowledge all known streaming interactive proofs are based on either of these tools, and indeed, this allows us to obtain zero-knowledge SIPs for central streaming problems such as index, point and range queries, median, frequency moments, and inner product. Our protocols are efficient in terms of time and space, as well as communication: the verifier algorithm's space complexity is $\mathrm{polylog}(n)$ and, after a non-interactive setup that uses a random string of near-linear length, the remaining parameters are $n^{o(1)}$. En route, we develop an algorithmic toolkit for designing zero-knowledge data stream protocols, consisting of an algebraic streaming commitment protocol and a temporal commitment protocol.Our analyses rely on delicate algebraic and information-theoretic arguments and reductions from average-case communication complexity.

翻译：流式交互证明（SIPs）允许一个空间受限的算法，通过单次访问海量数据流，并与一个强大但不可信的证明者进行通信，来验证需要大量空间的计算。本研究开创了数据流零知识证明的探索。我们定义了流式环境下的零知识概念，并为流式交互证明文献中的两个核心算法构建模块——和校验与多项式求值协议——构造了零知识SIP。据我们所知，所有已知的流式交互证明均基于这两种工具之一；事实上，这使我们能够为核心流式问题（如索引、点查询、范围查询、中位数、频率矩和内积）获得零知识SIP。我们的协议在时间、空间以及通信方面均高效：验证者算法的空间复杂度为 $\mathrm{polylog}(n)$，并且在使用近线性长度随机串进行非交互式设置后，其余参数为 $n^{o(1)}$。在此过程中，我们开发了一个用于设计零知识数据流协议的算法工具包，包含一个代数流式承诺协议和一个时序承诺协议。我们的分析依赖于精细的代数和信息论论证，以及平均情况通信复杂度的归约。