Fast Implementation of Lattice Trapdoors Based on Gadget Sampling

抄録

Lattice trapdoors can be used to construct advanced cryptographic applications, such as group signatures, attribute-based encryption, and fully homomorphic encryption. The current state-of-the-art implementation of lattice trapdoors is based on the gadget sampling algorithm (Genise and Miccianio, Eurocrypt 2018), which can be split into the online phase and the offline phase. However, for fixed-dimensional lattices, the integer discrete Gaussian sampler has become a performance bottleneck for lattice trapdoors. In this work, we propose a perturbed gadget sampling algorithm (PGSample) and introduce an implementation of a sampler utilizing a reversed cumulative distribution table (SampleI-RCDT). This approach optimizes sampling performance while facilitating efficient trapdoor implementations. For different parameter sets, our online phase uses desktop-level CPU execution times as fast as 0.25ms. Compared to previous work, our PGSample-based trapdoor outperforms previous methods by 43.3% to 46.8% overall and achieves a 5.5×-6.2× speedup in the online phase. In conclusion, this work provides a more practical and flexible solution for distributed cryptosystems and constrained devices.