Lattice reduction for modules, or how to reduce ModuleSVP to ModuleSVP

DOI10.1007/978-3-030-56880-1_8zbMath1504.94174OpenAlexW2982522610MaRDI QIDQ2096523

Tamalika Mukherjee, Noah Stephens-Davidowitz

Publication date: 9 November 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-56880-1_8

lattice reduction algorithms module lattices

Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16) Lattices and convex bodies (number-theoretic aspects) (11H06)

Related Items (3)

Application of automorphic forms to lattice problems ⋮ Just how hard are rotations of \(\mathbb{Z}^n\)? Algorithms and cryptography with the simplest lattice ⋮ Lattice reduction for modules, or how to reduce ModuleSVP to ModuleSVP

Cites Work

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A generalization of the LLL-algorithm over Euclidean rings or orders
The LLL algorithm. Survey and applications
On Lovász' lattice reduction and the nearest lattice point problem
Factoring polynomials with rational coefficients
Lattice basis reduction: Improved practical algorithms and solving subset sum problems
Lattice reductions over Euclidean rings with applications to cryptanalysis
Lattice reduction for modules, or how to reduce ModuleSVP to ModuleSVP
Slide reduction, revisited -- filling the gaps in SVP approximation
An LLL algorithm for module lattices
On the shortness of vectors to be found by the ideal-SVP quantum algorithm
Approx-SVP in ideal lattices with pre-processing
Worst-case to average-case reductions for module lattices
A Decade of Lattice Cryptography
Practical, Predictable Lattice Basis Reduction
Ring-LWE in Polynomial Rings
Making NTRU as Secure as Worst-Case Problems over Ideal Lattices
Trapdoors for hard lattices and new cryptographic constructions
On Ideal Lattices and Learning with Errors over Rings
Efficient Public Key Encryption Based on Ideal Lattices
Complex Lattice Reduction Algorithm for Low-Complexity Full-Diversity MIMO Detection
Short Bases of Lattices over Number Fields
Pseudorandomness of ring-LWE for any ring and modulus
Public-key cryptosystems from the worst-case shortest vector problem
Worst‐Case to Average‐Case Reductions Based on Gaussian Measures
Short Stickelberger Class Relations and Application to Ideal-SVP
Recovering Short Generators of Principal Ideals in Cyclotomic Rings
Theory of Cryptography
On lattices, learning with errors, random linear codes, and cryptography

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