Short Bases of Lattices over Number Fields

DOI10.1007/978-3-642-14518-6_15zbMath1260.11084OpenAlexW2113579323MaRDI QIDQ4931647

Damien Stehlé, Claus Fieker

Publication date: 29 September 2010

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-14518-6_15

zbMATH Keywords

LLL algorithmBosma-Pohst-Cohen Hermite normal formeffective variant of Minkowski's second theorem for lattices over number fieldsShort bases of lattices

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Algebraic numbers; rings of algebraic integers (11R04)

Related Items

Algebraic number fields and the LLL algorithm ⋮ On the hardness of the NTRU problem ⋮ The special case of cyclotomic fields in quantum algorithms for unit groups ⋮ Reductions from module lattices to free module lattices, and application to dequantizing module-LLL ⋮ Subfield algorithms for ideal- and module-SVP based on the decomposition group ⋮ On the computation of the HNF of a module over the ring of integers of a number field ⋮ Storage efficient algorithm for Hermite normal form using LLL ⋮ Ideal forms of Coppersmith's theorem and Guruswami-Sudan list decoding ⋮ Explicit $n$-descent on elliptic curves III. Algorithms ⋮ Determination of all rational preperiodic points for morphisms of PN ⋮ Lattice reduction for modules, or how to reduce ModuleSVP to ModuleSVP ⋮ Worst-case to average-case reductions for module lattices

Uses Software

• Magma

Cites Work

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