About: Lattice sieving     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Rule105846932, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon
http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FLattice_sieving&invfp=IFP_OFF&sas=SAME_AS_OFF

Lattice sieving is a technique for finding smooth values of a bivariate polynomial over a large region. It is almost exclusively used in conjunction with the number field sieve. The original idea of the lattice sieve came from John Pollard. The algorithm implicitly involves the ideal structure of the number field of the polynomial; it takes advantage of the theorem that any prime ideal above some rational prime p can be written as . One then picks many prime numbers q of an appropriate size, usually just above the factor base limit, and proceeds by

AttributesValues
rdf:type
rdfs:label
  • Lattice sieving (en)
rdfs:comment
  • Lattice sieving is a technique for finding smooth values of a bivariate polynomial over a large region. It is almost exclusively used in conjunction with the number field sieve. The original idea of the lattice sieve came from John Pollard. The algorithm implicitly involves the ideal structure of the number field of the polynomial; it takes advantage of the theorem that any prime ideal above some rational prime p can be written as . One then picks many prime numbers q of an appropriate size, usually just above the factor base limit, and proceeds by (en)
dcterms:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
sameAs
dbp:wikiPageUsesTemplate
has abstract
  • Lattice sieving is a technique for finding smooth values of a bivariate polynomial over a large region. It is almost exclusively used in conjunction with the number field sieve. The original idea of the lattice sieve came from John Pollard. The algorithm implicitly involves the ideal structure of the number field of the polynomial; it takes advantage of the theorem that any prime ideal above some rational prime p can be written as . One then picks many prime numbers q of an appropriate size, usually just above the factor base limit, and proceeds by For each q, list the prime ideals above q by factorising the polynomial f(a,b) over For each of these prime ideals, which are called 'special 's, construct a reduced basis for the lattice L generated by ; set a two-dimensional array called the to zero.For each prime ideal in the factor base, construct a reduced basis for the sublattice of L generated byFor each element of that sublattice lying within a sufficiently large sieve region, add to that entry.Read out all the entries in the sieve region with a large enough value For the number field sieve application, it is necessary for two polynomials both to have smooth values; this is handled by running the inner loop over both polynomials, whilst the special-q can be taken from either side. (en)
prov:wasDerivedFrom
page length (characters) of wiki page
foaf:isPrimaryTopicOf
is Link from a Wikipage to another Wikipage of
is Wikipage redirect of
is foaf:primaryTopic of
Faceted Search & Find service v1.17_git139 as of Feb 29 2024


Alternative Linked Data Documents: ODE     Content Formats:   [cxml] [csv]     RDF   [text] [turtle] [ld+json] [rdf+json] [rdf+xml]     ODATA   [atom+xml] [odata+json]     Microdata   [microdata+json] [html]    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 50 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software