Streaming interactive proofs

Abstract

An interactive proof is a conversation between a powerful machine, the ‘prover’, and a ‘verifier’ with low resources. The aim of the conversation is for the prover to convince the verifier about the output of a function (that is computationally or space intensive to evaluate) over some shared data set. The concept of streaming interactive proofs (SIPs) considers a verifier with very small space, who streams the shared data, and then engages in an interactive protocol with the prover. Our work begins by looking to improve protocols for the practical verification of outsourced data analysis. We explore non-interactive and multi-round protocols for vector and matrix multiplications and analyse the real-world practicality of these approaches. We demonstrate how these protocols can be used in data analysis, considering the numerical concerns when rounding is required. We investigate the costs for the verifier, while trying to keep the overheads for the prover at a minimum, and discuss bottlenecks. Finally, we introduce the entirely new concept of Streaming Zero Knowledge for interactive proofs, which is the adaptation of regular SIPs where now the verifier learns no additional information about the data set besides the truth of the statement the prover is trying to prove. We show several examples and build up a powerful multipurpose protocol in order to showcase the strengths of this new model