About: Ideal lattice

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Ideal lattice Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/c/9GRVExBrZx

In discrete mathematics, ideal lattices are a special class of lattices and a generalization of . Ideal lattices naturally occur in many parts of number theory, but also in other areas. In particular, they have a significant place in cryptography. Micciancio defined a generalization of cyclic lattices as ideal lattices. They can be used in cryptosystems to decrease by a square root the number of parameters necessary to describe a lattice, making them more efficient. Ideal lattices are a new concept, but similar lattice classes have been used for a long time. For example, cyclic lattices, a special case of ideal lattices, are used in NTRUEncrypt and NTRUSign.

Attributes	Values
rdfs:label	Ideal lattice (en) Идеальная решётка (ru)
rdfs:comment	Идеальная решётка — определённая математическая структура, которая используется для уменьшения числа параметров, необходимых для описания решёток (представляющих собой свободные коммутативные группы конечного ранга). Данный вид решёток часто встречается во многих областях математики, в частности, в разделе теории чисел. Таким образом идеальные решётки более эффективны в применении, чем другие решётки, применяющихся в криптографии. Идеальные решётки используются в криптографических системах с открытым ключом NTRUEncrypt и NTRUSign для построения эффективных криптографических примитивов. Также идеальные решётки составляют фундаментальную основу квантовой криптографии, которая защищает от атак, связанных с квантовыми компьютерами. (ru) In discrete mathematics, ideal lattices are a special class of lattices and a generalization of . Ideal lattices naturally occur in many parts of number theory, but also in other areas. In particular, they have a significant place in cryptography. Micciancio defined a generalization of cyclic lattices as ideal lattices. They can be used in cryptosystems to decrease by a square root the number of parameters necessary to describe a lattice, making them more efficient. Ideal lattices are a new concept, but similar lattice classes have been used for a long time. For example, cyclic lattices, a special case of ideal lattices, are used in NTRUEncrypt and NTRUSign. (en)
dcterms:subject	Number theory Lattice-based cryptography Post-quantum cryptography
Wikipage page ID	30628437 (xsd:integer)
Wikipage revision ID	1099938409 (xsd:integer)
Link from a Wikipage to another Wikipage	Monic polynomial Cyclotomic polynomial Vector space Integer lattice Quotient ring Complex number Cryptographic hash function Cryptography Linear time Collision resistance Hardness of approximation Ideal (ring theory) Post-quantum cryptography Public-key cryptography Hash collision Irreducible polynomial Lattice-based cryptography Lattice (group) Lattice problem Learning with errors Linear independence Open problem SWIFFT Adjugate matrix Number theory Number theory Digital signature Fast Fourier transform Isomorphism Ring (mathematics) Invertible matrix Prime number Ring Learning with Errors Chinese remainder theorem Hermite normal form Homomorphic encryption Lattice-based cryptography Post-quantum cryptography Polynomial ring Circulant matrix Free abelian group Group isomorphism Polynomial time RSA (algorithm) Shortest vector problem Short integer solution problem NTRUEncrypt NTRUSign Ring learning with errors key exchange dbr:Cyclic_lattice
sameAs	Ideal lattice Ideal lattice Ideal lattice
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Short_description
has abstract	In discrete mathematics, ideal lattices are a special class of lattices and a generalization of . Ideal lattices naturally occur in many parts of number theory, but also in other areas. In particular, they have a significant place in cryptography. Micciancio defined a generalization of cyclic lattices as ideal lattices. They can be used in cryptosystems to decrease by a square root the number of parameters necessary to describe a lattice, making them more efficient. Ideal lattices are a new concept, but similar lattice classes have been used for a long time. For example, cyclic lattices, a special case of ideal lattices, are used in NTRUEncrypt and NTRUSign. Ideal lattices also form the basis for quantum computer attack resistant cryptography based on the Ring Learning with Errors. These cryptosystems are provably secure under the assumption that the shortest vector problem (SVP) is hard in these ideal lattices. (en) Идеальная решётка — определённая математическая структура, которая используется для уменьшения числа параметров, необходимых для описания решёток (представляющих собой свободные коммутативные группы конечного ранга). Данный вид решёток часто встречается во многих областях математики, в частности, в разделе теории чисел. Таким образом идеальные решётки более эффективны в применении, чем другие решётки, применяющихся в криптографии. Идеальные решётки используются в криптографических системах с открытым ключом NTRUEncrypt и NTRUSign для построения эффективных криптографических примитивов. Также идеальные решётки составляют фундаментальную основу квантовой криптографии, которая защищает от атак, связанных с квантовыми компьютерами. (ru)
prov:wasDerivedFrom	wikipedia-en:Ideal_lattice?oldid=1099938409&ns=0
page length (characters) of wiki page	37637 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Ideal_lattice
is Link from a Wikipage to another Wikipage of	Ideal lattice cryptography Ideal Lattices and Cryptography
is Wikipage redirect of	Ideal lattice cryptography Ideal Lattices and Cryptography
is foaf:primaryTopic of	wikipedia-en:Ideal_lattice

Faceted Search & Find service v1.17_git147 as of Sep 06 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3332 as of Dec 5 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 60 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software