Function-Dependent Commitments for Verifiable Multi-party Computation

Abstract

In cloud computing, delegated computing raises the security issue of guaranteeing data authenticity during a remote computation. Existing solutions do not simultaneously provide fast correctness verification, strong security properties, and information-theoretic confidentiality. We introduce a novel approach, in the form of function-dependent commitments, that combines these strengths. We also provide an instantiation of function-dependent commitments for linear functions that is unconditionally, i.e. information-theoretically, hiding and relies on standard hardness assumptions. This powerful construction can for instance be used to build verifiable computing schemes providing information-theoretic confidentiality. As an example, we introduce a verifiable multi-party computation scheme for shared data providing public verifiability and unconditional privacy towards the servers and parties verifying the correctness of the result. Our scheme can be used to perform verifiable computations on secret shares while requiring only a single party to compute the audit data for verification. Furthermore, our verification procedure is asymptotically even more efficient than performing operations locally on the shared data. Thus, our solution improves the state of the art for authenticated computing, verifiable computing and multi-party computation.