Privacy-preserving and verifiable protocols for scientific computation outsourcing to the cloud

• Point out a problem in a previous linear equation outsourcing protocol.
• Propose new and efficient protocols for linear equation solving and linear programming outsourcing to the cloud.
• New protocols improve the performance of previous protocols significantly.
• Experimental results validate the new protocols.

Computation outsourcing to the cloud has become a popular application in the age of cloud computing. Recently, two protocols for secure outsourcing scientific computations, i.e., linear equation solving and linear programming solving, to the cloud were proposed. In this paper, we improve the work by proposing new protocols that achieve significant performance gains. For linear equation solving outsourcing, we achieve the improvement by proposing a completely new protocol. The new protocol employs some special linear transformations and there are no homomorphic encryptions and interactions between the client and the cloud, compared with the previous protocol. For linear programming outsourcing, we achieve the improvement by reformulating the linear programming problem in the standard and natural form. We also introduce a method to reduce the key size by using a pseudorandom number generator. The design of the newly proposed protocols also sheds some insight on constructing secure outsourcing protocols for other scientific computations. Comparisons between our protocols and the previous protocols are given, which demonstrate significant improvements of our proposed protocols. We also carry out numerical experiments to validate the efficiency of our protocols for secure linear equation solving and linear programming outsourcing.