Cloud computing has become a dominant paradigm for outsourcing computationally intensive tasks. However, the lack of transparency in remote execution poses significant challenges to integrity and trust. Verifiable computation (VC) mitigates these issues by enabling clients to efficiently verify outsourced results. Existing VC schemes often incur high verification costs, scale poorly, and exhibit low computational efficiency. We propose the Parallel and Verifiable Polynomial Computation (PVPC) scheme, designed for secure, privacy-preserving, and scalable polynomial evaluation in heterogeneous cloud-edge environments. PVPC reformulates polynomial evaluation as matrix-vector operations combined with random sparse blinding, enabling parallel execution across multiple sub-servers while preserving input privacy. It achieves sublinear complexity in the polynomial degree through row-wise factorization and enables aggregated batch verification via bilinear pairings, thereby reducing per-task verification overhead. We present formal correctness and security proofs under the Computational Diffie-Hellman assumption, and evaluate PVPC against state-of-the-art VC protocols. Experimental results show that PVPC substantially outperforms existing schemes in computation, verification, and recovery phases-particularly for high-degree polynomials-while maintaining practical communication costs. These features make PVPC well-suited for large-scale, latency-sensitive, and distributed verifiable computing applications.

Haze and fog, as severe weather conditions, have absorbing and scattering effects on the optical images, severely affecting image quality. Polarization-based dehazing algorithms can estimate the original radiance distribution of the scene through the polarization of skylight and transmitted light. However, current traditional methods lack consideration for the polarization of transmitted light, and the datasets required for deep learning-based methods are difficult to obtain. This paper proposes a polarized haze image synthesis method that can generate scene intensity and polarization after passing through different distances and concentrations from existing DoFP images, Specially, we equate the attenuation of the scattering medium to a superposition of a series of Mueller matrices, and in combination with the atmospheric attenuation model, which thoroughly integrates both intensity characteristics and polarization properties. We establish a comprehensive polarization dataset for image dehazing, including 300 sets of simulated data, 40 sets real world data from artificial scenes with haze-free ground truth and 40 sets real world data from urban scenes. The network model trained on our simulated dataset demonstrates the effectiveness of the simulation method in testing experiments.