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- Lattice_sieving 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 sieve region to zero. For each prime ideal in the factor base, construct a reduced basis for the sublattice of L generated by For 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 valueFor 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.".
- Lattice_sieving wikiPageID "14729575".
- Lattice_sieving wikiPageRevisionID "416212276".
- Lattice_sieving hasPhotoCollection Lattice_sieving.
- Lattice_sieving subject Category:Integer_factorization_algorithms.
- Lattice_sieving type Abstraction100002137.
- Lattice_sieving type Act100030358.
- Lattice_sieving type Activity100407535.
- Lattice_sieving type Algorithm105847438.
- Lattice_sieving type Event100029378.
- Lattice_sieving type IntegerFactorizationAlgorithms.
- Lattice_sieving type Procedure101023820.
- Lattice_sieving type PsychologicalFeature100023100.
- Lattice_sieving type Rule105846932.
- Lattice_sieving type YagoPermanentlyLocatedEntity.
- Lattice_sieving 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 .".
- Lattice_sieving label "Lattice sieving".
- Lattice_sieving sameAs m.03gvtsx.
- Lattice_sieving sameAs Q17079625.
- Lattice_sieving sameAs Q17079625.
- Lattice_sieving sameAs Lattice_sieving.
- Lattice_sieving wasDerivedFrom Lattice_sieving?oldid=416212276.
- Lattice_sieving isPrimaryTopicOf Lattice_sieving.