Verification protocols with sub-linear communication for polynomial matrix operations. (July 2021)

• Record Type: Journal Article
• Authors: Lucas, David; Neiger, Vincent; Pernet, Clément; Roche, Daniel S.; Rosenkilde, Johan
• Is Part Of: Journal of symbolic computation. Volume 105(2021)
• Page Start: 165
• Page End: 198
• Publication Date: 2021-07
• Subjects: Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.06.006
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We design and analyze new protocols to verify the correctness of various computations on matrices over the ring F [ x ] of univariate polynomials over a field F . For the sake of efficiency, and because many of the properties we verify are specific to matrices over a principal ideal domain, we cannot simply rely on previously-developed linear algebra protocols for matrices over a field. Our protocols are interactive, often randomized, and feature a constant number of rounds of communication between the Prover and Verifier. We seek to minimize the communication cost so that the amount of data sent during the protocol is significantly smaller than the size of the result being verified, which can be useful when combining protocols or in some multi-party settings. The main tools we use are reductions to existing linear algebra verification protocols and a new protocol to verify that a given vector is in the F [ x ] -row space of a given matrix.