Quantum algorithms for attacking hardness assumptions in classical and post‐quantum cryptography

JF Biasse, X Bonnetain, E Kirshanova… - IET Information …, 2023‏ - Wiley Online Library
In this survey, the authors review the main quantum algorithms for solving the computational
problems that serve as hardness assumptions for cryptosystem. To this end, the authors …

Differentially private clustering: Tight approximation ratios

B Ghazi, R Kumar… - Advances in Neural …, 2020‏ - proceedings.neurips.cc
We study the task of differentially private clustering. For several basic clustering problems,
including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient …

Improved provable reduction of ntru and hypercubic lattices

H Bambury, PQ Nguyen - International Conference on Post-Quantum …, 2024‏ - Springer
Lattice-based cryptography typically uses lattices with special properties to improve
efficiency. We show how blockwise reduction can exploit lattices with special geometric …

Slide reduction, revisited—filling the gaps in SVP approximation

D Aggarwal, J Li, PQ Nguyen… - Annual International …, 2020‏ - Springer
We show how to generalize Gama and Nguyen's slide reduction algorithm STOC'08 for
solving the approximate Shortest Vector Problem over lattices (SVP) to allow for arbitrary …

Fine-grained hardness of CVP (P)—Everything that we can prove (and nothing else)

D Aggarwal, H Bennett, A Golovnev… - Proceedings of the 2021 …, 2021‏ - SIAM
We show a number of fine-grained hardness results for the Closest Vector Problem in the ℓp
norm (CVP p), and its approximate and non-uniform variants. First, we show that CVP p …

(gap/S) ETH hardness of SVP

D Aggarwal, N Stephens-Davidowitz - … of the 50th Annual ACM SIGACT …, 2018‏ - dl.acm.org
We prove the following quantitative hardness results for the Shortest Vector Problem in the ℓ
p norm (SVP_p), where n is the rank of the input lattice. For “almost all” p> p 0≈ 2.1397 …

Property-preserving hash functions for hamming distance from standard assumptions

N Fleischhacker, KG Larsen, M Simkin - … on the Theory and Applications of …, 2022‏ - Springer
Property-preserving hash functions allow for compressing long inputs x 0 and x 1 into short
hashes h (x 0) and h (x 1) in a manner that allows for computing a predicate P (x 0, x 1) …

Approximate CVPp in time 20.802 n

F Eisenbrand, M Venzin - Journal of Computer and System Sciences, 2022‏ - Elsevier
We show that a constant factor approximation of the shortest and closest lattice vector
problem in any ℓ p-norm can be computed in time 2 (0.802+ ε) n. This matches the currently …

Provable lattice reduction of  with blocksize n/2

L Ducas - Designs, Codes and Cryptography, 2024‏ - Springer
Abstract The Lattice Isomorphism Problem (LIP) is the computational task of recovering,
assuming it exists, an orthogonal linear transformation sending one lattice to another. For …

Exploiting the Symmetry of : Randomization and the Automorphism Problem

K Jiang, A Wang, H Luo, G Liu, Y Yu… - … Conference on the Theory …, 2023‏ - Springer
Z n is one of the simplest types of lattices, but the computational problems on its rotations,
such as Z SVP and Z LIP, have been of great interest in cryptography. Recent advances …