Measure inequalities and the transference theorem in the geometry of numbers

DOI10.1090/S0002-9939-2013-11744-2zbMath1329.11072OpenAlexW2041491345MaRDI QIDQ2862169

Chengliang Tian, Ming-Jie Liu, Guangwu Xu

Publication date: 14 November 2013

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2013-11744-2

zbMATH Keywords

convex bodyGaussian measureslattice-based cryptographytransference theorem

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Cryptography (94A60) Lattices and convex bodies (number-theoretic aspects) (11H06) Mean value and transfer theorems (11H60)

Related Items (2)

Discrete Gaussian measures and new bounds of the smoothing parameter for lattices ⋮ On a certain class of positive definite functions and measures on locally compact abelian groups and inner-product spaces

Cites Work

• Unnamed Item
• New bounds in some transference theorems in the geometry of numbers
• Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\)
• Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\). II: Application of \(K\)-convexity
• A new transference theorem in the geometry of numbers and new bounds for Ajtai's connection factor
• Lattice problems in NP ∩ coNP
• New lattice-based cryptographic constructions
• Worst‐Case to Average‐Case Reductions Based on Gaussian Measures
• On lattices, learning with errors, random linear codes, and cryptography

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