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Quantum algorithms for attacking hardness assumptions in classical and post‐quantum cryptography
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 …
problems that serve as hardness assumptions for cryptosystem. To this end, the authors …
Differentially private clustering: Tight approximation ratios
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 …
including Euclidean DensestBall, 1-Cluster, k-means, and k-median, we give efficient …
Improved provable reduction of ntru and hypercubic lattices
Lattice-based cryptography typically uses lattices with special properties to improve
efficiency. We show how blockwise reduction can exploit lattices with special geometric …
efficiency. We show how blockwise reduction can exploit lattices with special geometric …
Slide reduction, revisited—filling the gaps in SVP approximation
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 …
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)
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 …
norm (CVP p), and its approximate and non-uniform variants. First, we show that CVP p …
(gap/S) ETH hardness of SVP
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 …
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
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) …
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
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 …
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
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 …
assuming it exists, an orthogonal linear transformation sending one lattice to another. For …
Exploiting the Symmetry of : Randomization and the Automorphism Problem
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 …
such as Z SVP and Z LIP, have been of great interest in cryptography. Recent advances …