Exploiting the symmetry of \(\mathbb{Z}^n\): randomization and the automorphism problem
From MaRDI portal
Publication:6604873
DOI10.1007/978-981-99-8730-6_6zbMath1547.94377MaRDI QIDQ6604873
Could not fetch data.
Publication date: 13 September 2024
gradient descentlattice automorphismrandomized reduction\( \mathbb{Z}\)LIPcharacteristic vectors of the unimodular lattice
Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Lattice packing and covering (number-theoretic aspects) (11H31)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- How to generate random matrices from the classical compact groups
- Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
- Factoring polynomials with rational coefficients
- Computing isometries of lattices
- A \(2^{n/2}\)-time algorithm for \(\sqrt{n} \)-SVP and \(\sqrt{n} \)-Hermite SVP, and an improved time-approximation tradeoff for (H)SVP
- Slide reduction, revisited -- filling the gaps in SVP approximation
- Generating cryptographically-strong random lattice bases and recognizing rotations of \(\mathbb{Z}^n\)
- On the lattice isomorphism problem, quadratic forms, remarkable lattices, and cryptography
- Lattices with symmetry
- Finding Shortest Lattice Vectors in the Presence of Gaps
- A Decade of Lattice Cryptography
- Revisiting the Gentry-Szydlo Algorithm
- Solving the Shortest Vector Problem in 2 n Time Using Discrete Gaussian Sampling
- Complexity and algorithms for computing Voronoi cells of lattices
- The Subgroup Algorithm for Generating Uniform Random Variables
- Trapdoors for hard lattices and new cryptographic constructions
- Bonsai Trees, or How to Delegate a Lattice Basis
- Learning a Parallelepiped: Cryptanalysis of GGH and NTRU Signatures
- The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators
- Search-to-Decision Reductions for Lattice Problems with Approximation Factors (Slightly) Greater Than One
- A reverse Minkowski theorem
- Just Take the Average! An Embarrassingly Simple $2^n$-Time Algorithm for SVP (and CVP)
- A quantum algorithm for computing the unit group of an arbitrary degree number field
- Graph isomorphism in quasipolynomial time [extended abstract]
- On the Lattice Isomorphism Problem
- On the Lattice Isomorphism Problem
- Cryptography and Coding
- Classical hardness of learning with errors
- A canonical form for positive definite matrices
- Just how hard are rotations of \(\mathbb{Z}^n\)? Algorithms and cryptography with the simplest lattice
- Hull attacks on the lattice isomorphism problem
- \textsc{Hawk}: module LIP makes lattice signatures fast, compact and simple
This page was built for publication: Exploiting the symmetry of \(\mathbb{Z}^n\): randomization and the automorphism problem