Cloud Computing permits customers with limited computational resources to outsource massive-scale computational tasks to the cloud, where huge computational power can be easily utilised in an exceedingly pay-per-use manner. However, security is the most important concern that forestalls the wide adoption of computation outsourcing in the cloud, particularly when finish-user's confidential knowledge are processed and produced throughout the computation. Thus, secure outsourcing mechanisms are in great want to not only protect sensitive information by enabling computations with encrypted information, however conjointly defend customers from malicious behaviors by validating the computation result. Such a mechanism of general secure computation outsourcing was recently shown to be possible in theory, however to style mechanisms that are practically economical remains a terribly difficult drawback. Focusing on engineering computing and optimization tasks, this paper investigates secure outsourcing of widely applicable linear programming (LP) computations. In order to realize sensible potency, our mechanism design explicitly decomposes the LP computation outsourcing into public LP solvers running on the cloud and private LP parameters owned by the customer. The resulting flexibility allows us to explore appropriate security/potency tradeoff via higher-level abstraction of LP computations than the final circuit representation. In particular, by formulating private data owned by the customer for LP problem as a set of matrices and vectors, we can develop a group of economical privacy-preserving drawback transformation techniques, that permit customers to remodel original LP drawback into some random one whereas protecting sensitive input/output info. To validate the computation result, we tend to further explore the elemental duality theorem of LP computation and derive the mandatory and sufficient conditions that correct result should satisfy. Such result verification mechanism is very efficient and incurs shut-t- - o-zero additional value on each cloud server and customers. Extensive security analysis and experiment results show the immediate practicability of our mechanism design.

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