Public Cryptography Linear Programming Solver in Cloud Computing

Public-key cryptography refers to a cryptographic system requiring two separate keys, one of which is secret and one of which is public.Cloud Computing has great potential of providing robust computational power to the society at reduced cost. It enables customers with limited computational resources to outsource their large computation workloads to the cloud, and economically enjoy the massive computational power, bandwidth, storage, and even appropriate software that can be shared in a pay-per-use manner. Despite the tremendous benefits, security is the primary obstacle that prevents the wide adoption of this promising computing model, especially for customers when their confidential data are consumed and produced during the computation. Treating the cloud as an intrinsically insecure computing platform from the viewpoint of the cloud customers, we must design mechanisms that not only protect sensitive information by enabling computations with encrypted data, but also protect customers from malicious behaviors by enabling the validation of the computation result. Focusing on engineering computing and optimization tasks, we investigates secure outsourcing of widely applicable linear programming (LP) computations. In order to achieve practical efficiency, 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. To validate the computation result, we explore the fundamental duality theorem of LP computation and derive the necessary and sufficient conditions that correct result must satisfy. In the proposed algorithm, the robustness preference of the output given by the server is checked by the client, whether the server is given the correct output. Whether the cloud is giving the correct result we also try to device the robust algorithm for numerical stability.