Protecting Function Privacy and Input Privacy in the Publicly Verifiable Outsourcing Computation of Polynomial Functions

With the prevalence of cloud computing, the outsourcing of computation has gained significant attention. Clients with limited computing power often outsource complex computing tasks to the cloud to save on computing resources and costs. In outsourcing the computation of functions, a function owner delegates a cloud server to perform the function's computation on the input received from the user. There are three primary security concerns associated with this process: protecting function privacy for the function owner, protecting input privacy for the user and guaranteeing that the cloud server performs the computation correctly. Existing works have only addressed privately verifiable outsourcing computation with privacy or publicly verifiable outsourcing computation without input privacy or function privacy. By using the technologies of homomorphic encryption, proxy re-encryption and verifiable computation, we propose the first publicly verifiable outsourcing computation scheme that achieves both input privacy and function privacy for matrix functions, which can be extended to arbitrary multivariate polynomial functions. We additionally provide a faster privately verifiable method. Moreover, the function owner retains control over the function.