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.

As the popularity of outsourced computation increases, questions of accuracy and trust between the client and the cloud computing services become ever more relevant. Our work aims to provide fast and practical methods to verify analysis of large data sets, where the client’s computation and memory costs are kept to a minimum. Our verification protocols are based on defining ’proofs’ which are easy to create and check. These add only a small overhead to reporting the result of the computation itself. We build up a series of protocols for elementary statistical methods, to create more complex protocols for Ordinary Least Squares, Principal Component Analysis and Linear Discriminant Analysis, and show them to be very efficient in practice.

Much of computer science involves problems where it is considered to be easier to check that an answer is correct than to find a correct answer (the complexity class NP). In this talk, we outline results that apply this notion to checking outsourced computations for data analytics.