Efficient Key Generation on Lattice Cryptography for Privacy Protection in Mobile IoT Crowdsourcing

To face urgent concern of privacy leakage on mobile crowdsourcing, some lattice-based cryptographic (LBC) schemes have been applied to the cloud-fog-edge data sharing platform for privacy protection. As an important factor of LBC's security, current key generation usually involves preimage Gaussian sampling for lattice trapdoor (PGS-LT) to sample short preimage vector from dual lattice. However, there lacks researches on the implementation of PGS-LT according to entities' computation and storage capacities. To address this issue, we present a fast double-perturbation scheme that is applied to the cloud-fog-edge data sharing platform. First, we design a fast spherical G-lattice sampling algorithm, including two samplers: 1) G-perturbation sampler and 2) G-lattice sampler. Among them, the fast nonspherical G-lattice sampling algorithm is extended to arbitrary bases, and deployed on the G-lattice sampler. Meanwhile, the G-perturbation sampler is designed to sample G-perturbation for converting the nonspherical distribution of output G-lattice vector to the spherical one. Second, we optimize the assignment of computational tasks in PGS-LT by considering entities' abilities in the cloud-fog-edge platform. Moreover, we analyze three types of delegated preimage sampling in terms of Gaussian quality and complexity. The analysis and experimental results show that fast spherical G-lattice sampling provides high-Gaussian quality of output vector. Meanwhile, in the aspect of complexity, the G-perturbation sampler has lower time and space complexity than the existing works. The G-lattice sampler remains good performance as it only involves extra integer multiplications in linear time complexity.