Paper Title
Privacy-Preserving Federated Compressive Sensing with Quantum-Resistant Security

Abstract
The rapid expansion of edge–cloud computing has enabled large-scale data collection and processing for various applications, including the Internet of Things (IoT), smart healthcare, and intelligent transportation systems. However, ensuring data privacy and security during distributed signal reconstruction remains a significant challenge, particularly with the emerging threats posed by quantum computing to traditional cryptographic systems. This paper proposes a novel framework called Quantum-Resistant Federated Compressive Sensing (QRFCS), which integrates lattice-based post-quantum cryptography with federated compressive sensing to enable secure and privacy-preserving signal reconstruction in edge–cloud environments. In this framework, edge devices perform local compressive measurements on high-dimensional data to reduce communication overhead, and the compressed data is encrypted using lattice-based homomorphic encryption before being securely aggregated in the cloud, offering strong resistance to quantum attacks. The federated reconstruction process facilitates collaborative signal recovery without exposing raw data to the cloud or participating devices, while the incorporation of differential privacy further safeguards against inference attacks without significantly affecting reconstruction accuracy. Experimental evaluations on IoT and smart city datasets demonstrate that QRFCS achieves high reconstruction fidelity with substantially lower computational and communication costs compared to traditional fully homomorphic encryption-based methods. Additionally, security analysis confirms its robustness against both classical and quantum adversaries, providing a scalable and future-proof solution for secure data processing in next-generation edge–cloud systems. Keywords - Post-Quantum Cryptography, Federated Compressive Sensing, Edge–Cloud Security, Privacy-Preserving Data Reconstruction, Lattice-Based Encryption.