Thijs Laarhoven

Sieving for Shortest Vectors in Lattices Using Angular Locality-Sensitive Hashing

By replacing the brute-force list search in sieving algorithms with Charikar’s angular locality-sensitive hashing (LSH) method, we get both theoretical and practical speedups for solving the shortest vector problem (SVP) on lattices. Combining angular LSH with a variant of Nguyen and Vidick’s heuristic sieve algorithm, we obtain heuristic time and space complexities for solving SVP of \(2^{0.3366n + o(n)}\) and \(2^{0.2075n + o(n)}\) respectively, while combining the same hash family with Micciancio and Voulgaris’ GaussSieve algorithm leads to an algorithm with (conjectured) heuristic time and space complexities of \(2^{0.3366n + o(n)}\). Experiments with the GaussSieve-variant show that in moderate dimensions the proposed HashSieve algorithm already outperforms the GaussSieve, and the practical increase in the space complexity is much smaller than the asymptotic bounds suggest, and can be further reduced with probing. Extrapolating to higher dimensions, we estimate that a fully optimized and parallelized implementation of the GaussSieve-based HashSieve algorithm might need a few core years to solve SVP in dimension 130 or even 140.

Optimal hashing-based time-space trade-offs for approximate near neighbors

[See the paper for the full abstract.] We show tight upper and lower bounds for time-space trade-offs for the

Parallel (Probable) Lock-Free Hash Sieve: A Practical Sieving Algorithm for the SVP

c

Solving the Shortest Vector Problem in Lattices Faster Using Quantum Search

-Approximate Near Neighbor Search problem. For the

A Parallel Variant of LDSieve for the SVP on Lattices

d

Speed-Ups and Time–Memory Trade-Offs for Tuple Lattice Sieving

-dimensional Euclidean space and

A Practical View of the State-of-the-Art of Lattice-Based Cryptanalysis

n

Progressive Lattice Sieving

-point datasets, we develop a data structure with space

Optimal Sequential Fingerprinting: Wald vs. Tardos

n^{1 + \rho_u + o(1)} + O(dn)

Post-Quantum Cryptography - PQC 2013

and query time