Cloud computing permits customers with restricted computational resources to outsource giant-scale computational tasks to the cloud, where massive computational power will be simply utilized in a very 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 data are processed and produced throughout the computation. Thus, secure outsourcing mechanisms are in nice would like to not only defend sensitive data by enabling computations with encrypted knowledge, however additionally shield 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, but to design 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 practical efficiency, our mechanism design explicitly decomposes the LP computation outsourcing into public LP solvers running on the cloud and non-public LP parameters owned by the customer. The resulting flexibility allows us to explore appropriate security/efficiency tradeoff via higher-level abstraction of LP computations than the general circuit representation. In particular, by formulating private data owned by the customer for LP problem as a set of matrices and vectors, we have a tendency to can develop a group of economical privacy-preserving downside transformation techniques, that enable customers to remodel original LP problem into some random one while protecting sensitive input/output info. To validate the computation result, we have a tendency to any explore the elemental duality theorem of LP computation and derive the mandatory and sufficient conditions that correct result must satisfy. Such result verification mechanism is extraordinarily economical and incurs close-t- - o-zero extra value on each cloud server and customers. Extensive security analysis and experiment results show the immediate practicability of our mechanism style.
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