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Modern information technology is increasingly used in healthcare with the goal to improve and enhance medical services and to reduce costs. In this context, the outsourcing of computation and storage resources to general IT providers (cloud computing) has become very appealing . As cloud computing is becoming more mature data outsourcing in public cloud is also gaining momentum including sensitive information like personal data, health data, media files and government documents. For sensitive data which is outsourced in public cloud, its encrypted uploads are recommended thus narrowing its utility scope in terms of processing and evaluation. To evaluate user requests obliviously on public cloud over sensitive encrypted data, we have formalized a system which protects not only the privacy of data but also the evaluation process that is carried on the public cloud. Throughout the system execution the cloud server will learn nothing useful except the reply cardinality.

Recently, a new class of nonrecursive digital filters, which is called the threshold Boolean filter (TBF), has been introduced as an extension of stack filters. While a procedure for finding a TBF that yields a smaller mean absolute error (MAE) than an optimal stack filter is known, no efficient algorithm for finding the best TBF in the MAE sense is available at this time. As an alternative, the optimal TBF under the mean square error (MSE) criterion is considered in this paper. It is shown that the optimization problem can be formulated into a known problem: the minimisation of a pseudo-Boolean quadratic function, which is an NP-hard problem. In this paper, a numerical method embedded in a branch and bound algorithm is adopted to solve the minimization problem. Some computer experiments with real signals are performed, and the results of optimal threshold Boolean filtering are compared with those of linear FIR Wiener and optimal stack filters.