Trusted computation with an adversarial cloud

We consider the problem of computation in a cloud environment where either the data or the computation may be corrupted by an adversary. We assume that a small fraction of the data is stored locally at a client during the upload process to the cloud and that this data is trustworthy. We formulate the problem within a game theoretic framework where the client needs to decide an optimal fusion strategy using both non-trusted information from the cloud and local trusted data, given that the adversary on the cloud is trying to deceive the client by biasing the output to a different value/set of values. We adopt an Iterated Best Response (IBR) scheme for each player to update its action based on the opponent's announced computation. At each iteration, the cloud reveals its output to the client, who then computes the best response as a linear combination of its private local estimate and of the untrusted cloud output. We characterize equilibrium conditions for both the scalar and vector cases of the computed value of interest. Necessary and sufficient conditions for convergence for the IBR are derived and insightful geometric interpretations of such conditions is discussed for the vector case. Numerical results are presented showing the convergence conditions are relatively tight.