Efficient Interactive Proofs for Linear Algebra

Motivated by the growth in outsourced data analysis, we describe methods for verifying basic linear algebra operations performed by a cloud service without having to recalculate the entire result. We provide novel protocols in the streaming setting for inner product, matrix multiplication and vector-matrix-vector multiplication where the number of rounds of interaction can be adjusted to tradeoff space, communication, and duration of the protocol. Previous work suggests that the costs of these interactive protocols are optimized by choosing O(log n) rounds. However, we argue that we can reduce the number of rounds without incurring a significant time penalty by considering the total end-to-end time, so fewer rounds and larger messages are preferable. We confirm this claim with an experimental study that shows that a constant number of rounds gives the fastest protocol

Streaming interactive proofs

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

Efficient interactive proofs for linear algebra

Motivated by the growth in outsourced data analysis, we describe methods for verifying basic linear algebra operations performed by a cloud service without having to recalculate the entire result. We provide novel protocols in the streaming setting for inner product, matrix multiplication and vector-matrix-vector multiplication where the number of rounds of interaction can be adjusted to tradeoff space, communication, and duration of the protocol. Previous work suggests that the costs of these interactive protocols are optimized by choosing O(log n) rounds. However, we argue that we can reduce the number of rounds without incurring a significant time penalty by considering the total end-to-end time, so fewer rounds and larger messages are preferable. We confirm this claim with an experimental study that shows that a constant number of rounds gives the fastest protocol