HTML Microdata document

This HTML5 document contains 29 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

Prefix	IRI
dcterms	http://purl.org/dc/terms/
dbo	http://dbpedia.org/ontology/
foaf	http://xmlns.com/foaf/0.1/
n12	https://global.dbpedia.org/id/
rdfs	http://www.w3.org/2000/01/rdf-schema#
rdf	http://www.w3.org/1999/02/22-rdf-syntax-ns#
owl	http://www.w3.org/2002/07/owl#
wikipedia-en	http://en.wikipedia.org/wiki/
dbc	http://dbpedia.org/resource/Category:
prov	http://www.w3.org/ns/prov#
xsdh	http://www.w3.org/2001/XMLSchema#
wikidata	http://www.wikidata.org/entity/
dbr	http://dbpedia.org/resource/

Statements

Subject Item: dbr:Itō
dbo:wikiPageWikiLink: dbr:Itoh–Tsujii_inversion_algorithm

Subject Item: dbr:Itoh-Tsujii_inversion_algorithm
dbo:wikiPageWikiLink: dbr:Itoh–Tsujii_inversion_algorithm
dbo:wikiPageRedirects: dbr:Itoh–Tsujii_inversion_algorithm

Subject Item: dbr:Itoh–Tsujii_inversion_algorithm
rdfs:label: Itoh–Tsujii inversion algorithm
rdfs:comment: The Itoh–Tsujii inversion algorithm is used to invert elements in a finite field. It was introduced in 1988, first over GF(2m) using the normal basis representation of elements, however, the algorithm is generic and can be used for other bases, such as the polynomial basis. It can also be used in any finite field GF(pm). The algorithm is as follows: Input: A ∈ GF(pm)Output: A−1 1. * r ← (pm − 1)/(p − 1) 2. * compute Ar − 1 in GF(pm) 3. * compute Ar = Ar − 1 · A 4. * compute (Ar)−1 in GF(p) 5. * compute A−1 = (Ar)−1 · Ar −1 6. * return A−1
dcterms:subject: dbc:Finite_fields dbc:Computational_number_theory
dbo:wikiPageID: 1180190
dbo:wikiPageRevisionID: 1063675646
dbo:wikiPageWikiLink: dbc:Computational_number_theory dbr:Polynomial_basis dbr:Finite_field_arithmetic dbr:Normal_basis dbc:Finite_fields dbr:Finite_field
owl:sameAs: wikidata:Q17092776 n12:f8v7
dbo:abstract: The Itoh–Tsujii inversion algorithm is used to invert elements in a finite field. It was introduced in 1988, first over GF(2m) using the normal basis representation of elements, however, the algorithm is generic and can be used for other bases, such as the polynomial basis. It can also be used in any finite field GF(pm). The algorithm is as follows: Input: A ∈ GF(pm)Output: A−1 1. * r ← (pm − 1)/(p − 1) 2. * compute Ar − 1 in GF(pm) 3. * compute Ar = Ar − 1 · A 4. * compute (Ar)−1 in GF(p) 5. * compute A−1 = (Ar)−1 · Ar −1 6. * return A−1 This algorithm is fast because steps 3 and 5 both involve operations in the subfield GF(p). Similarly, if a small value of p is used, a lookup table can be used for inversion in step 4. The majority of time spent in this algorithm is in step 2, the first exponentiation. This is one reason why this algorithm is well suited for the normal basis, since squaring and exponentiation are relatively easy in that basis.
prov:wasDerivedFrom: wikipedia-en:Itoh–Tsujii_inversion_algorithm?oldid=1063675646&ns=0
dbo:wikiPageLength: 1877
foaf:isPrimaryTopicOf: wikipedia-en:Itoh–Tsujii_inversion_algorithm

Subject Item: dbr:Finite_field_arithmetic
dbo:wikiPageWikiLink: dbr:Itoh–Tsujii_inversion_algorithm

Subject Item: dbr:Itoh-Tsujii
dbo:wikiPageWikiLink: dbr:Itoh–Tsujii_inversion_algorithm
dbo:wikiPageRedirects: dbr:Itoh–Tsujii_inversion_algorithm

Subject Item: dbr:Itoh-Tsujii_algorithm
dbo:wikiPageWikiLink: dbr:Itoh–Tsujii_inversion_algorithm
dbo:wikiPageRedirects: dbr:Itoh–Tsujii_inversion_algorithm

Subject Item: dbr:Itoh-Tsujii_inversion
dbo:wikiPageWikiLink: dbr:Itoh–Tsujii_inversion_algorithm
dbo:wikiPageRedirects: dbr:Itoh–Tsujii_inversion_algorithm

Subject Item: wikipedia-en:Itoh–Tsujii_inversion_algorithm
foaf:primaryTopic: dbr:Itoh–Tsujii_inversion_algorithm