From secrecy to soundness: Efficient verification via secure computation

We study the problem of verifiable computation (VC) in which a computationally weak client wishes to delegate the computation of a function f on an input x to a computationally strong but untrusted server. We present new general approaches for constructing VC protocols, as well as solving the related problems of program checking and self-correcting. The new approaches reduce the task of verifiable computation to suitable variants of secure multiparty computation (MPC) protocols. In particular, we show how to efficiently convert the secrecy property of MPC protocols into soundness of a VC protocol via the use of a message authentication code (MAC). The new connections allow us to apply results from the area of MPC towards simplifying, unifying, and improving over previous results on VC and related problems. In particular, we obtain the following concrete applications: (1) The first VC protocols for arithmetic computations which only make a black-box use of the underlying field or ring; (2) a non-interactive VC protocol for boolean circuits in the preprocessing model, conceptually simplifying and improving the online complexity of a recent protocol of Gennaro et al. (Cryptology ePrint Archive: Report 2009/547); (3) NC⁰ self-correctors for complete languages in the complexity class NC¹ and various log-space classes, strengthening previous AC ⁰ correctors of Goldwasser et al. (STOC 2008).