Publicly Verifiable Polynomial Outsourcing Computation based on Secret Sharing

Outsourced computation allows clients with limited computational resources to offload function-based computations to more powerful but potentially untrusted servers.In this context, secret sharing can be used to protect the privacy of input data.Verifiable secret sharing, on the other hand, allows participants to verify the correctness of the results returned by the server, thus enhancing the security and reliability of the process.However, existing verifiable homomorphic secret sharing schemes have several limitations, including low computational efficiency, lack of public verifiability, and poor compactness.To address these issues, we propose a public-verifiable polynomial outsourced computation scheme based on secret sharing, which improves efficiency and allows users to publicly verify the results through secret sharing and verification techniques.The proposed scheme offers the following advantages: 1) it eliminates the need to encrypt secret shares, and improves computational efficiency; 2) it ensures public verifiability of the computation results.