The increasing massive data generated by various sources has given birth to big data analytics. Solving large-scale nonlinear programming problems (NLPs) is one important big data analytics task that has applications in many domains such as transport and logistics. However, NLPs are usually too computationally expensive for resource-constrained users. Fortunately, cloud computing provides an alternative and economical service for resource-constrained users to outsource their computation tasks to the cloud. However, one major concern with outsourcing NLPs is the leakage of user's private information contained in NLP formulations and results. Although much work has been done on privacy-preserving outsourcing of computation tasks, little attention has been paid to NLPs. In this paper, we for the first time investigate secure outsourcing of general large-scale NLPs with nonlinear constraints. A secure and efficient transformation scheme at the user side is proposed to protect user's private information; at the cloud side, generalized reduced gradient method is applied to effectively solve the transformed large-scale NLPs. The proposed protocol is implemented on a cloud computing testbed. Experimental evaluations demonstrate that significant time can be saved for users and the proposed mechanism has the potential for practical use.
Much work has been done on privacy-preserving outsourcing of computation-intensive tasks to the cloud. Some work focused on outsourcing arbitrary computation functions @cite_13 @cite_12 @cite_1 , mainly using fully homomorphic encryption (FHE) schemes such as @cite_18 . Although theoretical guarantees of privacy can be achieved with FHE, current FHE schemes have very high computation cost, making them impractical for large-scale computations such as large-scale NLPs addressed in this paper. Other work designed secure outsourcing protocols for specific problems, such as linear programming @cite_6 , system of equations @cite_19 , distributed linear programming @cite_9 , quadratic programming @cite_8 , and linear regression @cite_15 . Outsourcing basic mathematical computations has also been studied, such as matrix determinant computation @cite_7 , matrix inversion @cite_11 , and modular exponentiations @cite_3 . However, previous work mostly focused on linear systems and some other particular problems. Outsourcing NLPs has received little attention Very recently, we also studied securely outsourcing NLPs in our previous work @cite_10 , but that work only considers NLPs with equality constraints. Different from it, this paper addresses NLPs with inequality and equality constraints which are more complicated and general.
@cite_18 @cite_7 @cite_8 @cite_10 @cite_9 @cite_1 @cite_6 @cite_3 @cite_19 @cite_15 @cite_13 @cite_12 @cite_11
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We give improved protocols for the secure and private outsourcing of linear algebra computations, that enable a client to securely outsource expensive algebraic computations (like the multiplication of large matrices) to a remote server, such that the server learns nothing about the customer's private input or the result of the computation, and any attempted corruption of the answer by the server is detected with high probability. The computational work performed at the client is linear in the size of its input and does not require the client to locally carry out any expensive encryptions of such input. The computational burden on the server is proportional to the time complexity of the current practically used algorithms for solving the algebraic problem (e.g., proportional to n3 for multiplying two n x n matrices). The improvements we give are: (i) whereas the previous work required more than one remote server and assumed they do not collude, our solution works with a single server (but readily accommodates many, for improved performance); (ii) whereas the previous work required a server to carry out expensive cryptographic computations (e.g., homomorphic encryptions), our solution does not make use of any such expensive cryptographic primitives; and (iii) whereas in previous work collusion by the servers against the client revealed to them the client's inputs, our scheme is resistant to such collusion. As in previous work, we maintain the property that the scheme enables the client to detect any attempt by the server(s) at corruption of the answer, even when the attempt is collusive and coordinated among the servers. Cloud computing economically enables customers with limited computational resources to outsource large-scale computations to the cloud. However, how to protect customers' confidential data involved in the computations then becomes a major security concern. In this paper, we present a secure outsourcing mechanism for solving large-scale systems of linear equations (LE) in cloud. Because applying traditional approaches like Gaussian elimination or LU decomposition (aka. direct method) to such large-scale LE problems would be prohibitively expensive, we build the secure LE outsourcing mechanism via a completely different approach -- iterative method, which is much easier to implement in practice and only demands relatively simpler matrix-vector operations. Specifically, our mechanism enables a customer to securely harness the cloud for iteratively finding successive approximations to the LE solution, while keeping both the sensitive input and output of the computation private. For robust cheating detection, we further explore the algebraic property of matrix-vector operations and propose an efficient result verification mechanism, which allows the customer to verify all answers received from previous iterative approximations in one batch with high probability. Thorough security analysis and prototype experiments on Amazon EC2 demonstrate the validity and practicality of our proposed design. Cloud computing economically enables customers with limited computational resources to outsource large-scale computations to the cloud. However, how to protect customers' confidential data involved in the computations then becomes a major security concern. In this paper, we present a secure outsourcing mechanism for solving large-scale systems of linear equations (LE) in cloud. Because applying traditional approaches like Gaussian elimination or LU decomposition (aka. direct method) to such large-scale LEs would be prohibitively expensive, we build the secure LE outsourcing mechanism via a completely different approach&#x2014;iterative method, which is much easier to implement in practice and only demands relatively simpler matrix-vector operations. Specifically, our mechanism enables a customer to securely harness the cloud for iteratively finding successive approximations to the LE solution, while keeping both the sensitive input and output of the computation private. For robust cheating detection, we further explore the algebraic property of matrix-vector operations and propose an efficient result verification mechanism, which allows the customer to verify all answers received from previous iterative approximations in one batch with high probability. Thorough security analysis and prototype experiments on Amazon EC2 demonstrate the validity and practicality of our proposed design. Cloud computing enables customers with limited computational resources to outsource large-scale computational tasks to the cloud, where massive computational power can be easily utilized in a pay-per-use manner. However, security is the major concern that prevents the wide adoption of computation outsourcing in the cloud, especially when end-user's confidential data are processed and produced during the computation. Thus, secure outsourcing mechanisms are in great need to not only protect sensitive information by enabling computations with encrypted data, but also protect customers from malicious behaviors by validating the computation result. Such a mechanism of general secure computation outsourcing was recently shown to be feasible in theory, but to design mechanisms that are practically efficient remains a very challenging problem. Focusing on engineering computing and optimization tasks, this paper 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. 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 are able to develop a set of efficient privacy-preserving problem transformation techniques, which allow customers to transform original LP problem into some random one while protecting sensitive input output information. To validate the computation result, we further explore the fundamental duality theorem of LP computation and derive the necessary and sufficient conditions that correct result must satisfy. Such result verification mechanism is extremely efficient and incurs close-to-zero additional cost on both cloud server and customers. Extensive security analysis and experiment results show the immediate practicability of our mechanism design.