Approximate Voronoi cells for lattices, revisited
This work addresses the closest vector problem with preprocessing in lattice-based cryptography, providing incremental improvements in time-memory trade-offs for cryptographic applications.
The paper tackles the problem of determining exact asymptotics for the volume of approximate Voronoi cells in high-dimensional lattices, settling an open problem and resulting in improved upper bounds on time complexity for the randomized iterative slicer, with trade-offs achievable even with less than 2^{0.048d + o(d)} memory.
We revisit the approximate Voronoi cells approach for solving the closest vector problem with preprocessing (CVPP) on high-dimensional lattices, and settle the open problem of Doulgerakis-Laarhoven-De Weger [PQCrypto, 2019] of determining exact asymptotics on the volume of these Voronoi cells under the Gaussian heuristic. As a result, we obtain improved upper bounds on the time complexity of the randomized iterative slicer when using less than $2^{0.076d + o(d)}$ memory, and we show how to obtain time-memory trade-offs even when using less than $2^{0.048d + o(d)}$ memory. We also settle the open problem of obtaining a continuous trade-off between the size of the advice and the query time complexity, as the time complexity with subexponential advice in our approach scales as $d^{d/2 + o(d)}$, matching worst-case enumeration bounds, and achieving the same asymptotic scaling as average-case enumeration algorithms for the closest vector problem.