Einocchio: Efficiently Outsourcing Polynomial Computation With Verifiable Computation and Optimized Newton Interpolation

Cloud computing, as a promising service platform, has gained significant popularity in addressing emerging data privacy issues in applications such as machine learning and data mining. Researchers have proposed the verifiable computing that allows the cloud users to delegate their computation tasks to the cloud server. Then, the cloud server computes the cryptographic proofs that verify the correctness of the results, a process that is generally faster ompared to local manual computation. However, performing computation tasks or verifying the correctness of encrypted data, such as multivariate polynomial functions, remains a significant challenge. To solve this problem, we propose Einocchio: a verifiable computation scheme that combines the efficient Pinocchio system with homomorphic encryption, which allows the public verification of the computational results on the server side while ensuring data confidentiality and the results. Compared with the existing solutions, Einocchio does not reveal the client’s input. Furthermore, we extrapolate Einocchio by optimizing the Pinocchio’s quadratic arithmetic program component using a differential optimization method, which reduces the computational workload owing to the conversion from quadratic to linear complexity, thereby increasing the efficiency of the quadratic arithmetic program preprocessing stage. Security analysis demonstrates that Einocchio achieves IND-CPA security. Finally, the performance evaluation confirmed its effectiveness and suitability for cloud computing environments. Compared to the corresponding scheme based on Newton interpolation, Einocchio achieves a threefold greater computational efficiency, with the generation of interpolation polynomials for 50 data inputs occurring in a mere 0.31 ms, while simultaneously reducing the number of computations.