no code implementations • 10 Jul 2019 • Thijs Laarhoven
Lattice-based cryptography has recently emerged as a prominent candidate for secure communication in the quantum age.
no code implementations • 10 Jul 2019 • Thijs Laarhoven
In three and four dimensions, we numerically find that the tetrahedron, $5$-cell, and $16$-cell achieve the best query exponents, while in five or more dimensions orthoplices appear to outperform regular simplices, as well as the root lattice families $A_k$ and $D_k$.
1 code implementation • 19 Feb 2017 • Thijs Laarhoven
A celebrated technique for finding near neighbors for the angular distance involves using a set of \textit{random} hyperplanes to partition the space into hash regions [Charikar, STOC 2002].
Data Structures and Algorithms Computational Complexity Computational Geometry Cryptography and Security
1 code implementation • NeurIPS 2015 • Alexandr Andoni, Piotr Indyk, Thijs Laarhoven, Ilya Razenshteyn, Ludwig Schmidt
Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.