Consider a client who intends to perform a massive computing task comprsing a number of sub-tasks, while both storage and computation are outsourced by a third-party service provider. How could the client ensure the integrity and completeness of the computation result? Meanwhile, how could the assurance mechanism incur no disincentive, e.g., excessive communication cost, for any service provider or client to participate in such a scheme? We detail this problem and present a general model of execution assurance for massive computing tasks. A series of key features distinguish our work from existing ones: a) we consider the context wherein both storage and computation are provided by untrusted third parties, and client has no data possession; b) we propose a simple yet effective assurance model based on a novel integration of the machineries of data authentication and computational private information retrieval (cPIR); c) we conduct an analytical study on the inherent trade-offs among the verification accuracy, and the computation, storage, and communication costs.