Secure Collaborative Publicly Verifiable Computation

Publicly Verifiable Computation (PVC) enables computationally weak trusted sources to outsource several computations to some more powerful public untrusted clouds. On issuing a query, the public cloud replies the result of the function evaluation with a witness vouching for correctness of computation. This primitive requires high efficiency and public verifiability. However, existing PVC constructions all request trusted sources to know delegated function beforehand, and thus it fails to meet diverse requirements, especially outsourced target unknown need to be jointly computed among different entities in a privacy-preserving manner. To strengthen current PVC’s flexibility, we proposed a new primitive called Secure Collaborative PVC ( ${\mathcal {SCPVC}}$ ), where TTP is responsible only for initializing system parameter and publishing some information in its bulletin. After some rounds, the public cloud owns lots of functions outsourced in PVC ways. The private cloud works out an algebraic operation structure ${\mathcal {L}}$ , which involves some functions provided by public cloud and himself. Based on ${\mathcal {L}}$ , they jointly perform the protocol to generate the target function. At the end of the protocol, the public cloud obtains target function while not disclosing respective secrets. Due to the misbehavior of the public cloud, this mechanism allows the private cloud to check the integrity of target function and any client to verify the correctness of results. Our scheme without jointly computing is a typical existing PVC scheme. Therefore, our protocol is compatible with the prevailing publicly verifiable computation Scheme. Before investigating ${\mathcal {SCPVC}}$ , we tailored two secure two-party polynomial computation protocols using 1-out-of- ${l}$ Oblivious Transfer protocol as the main building block to $ {\mathcal {SCPVC}}$ . More preciously, polynomial multiplication protocol transforms two polynomials multiplication into another two addition such that the result of sum is equal to the result of multiplication. Similarly, polynomial addition protocol is as same as multiplication protocol converts two polynomials addition into another two multiplication.