About: Vectorial addition chain

An Entity of Type: SocialGroup107950920, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In mathematics, for positive integers k and s, a vectorial addition chain is a sequence V of k-dimensional vectors of nonnegative integers vi for −k + 1 ≤ i ≤ s together with a sequence w,such that v−k+1 = [1,0,0,...0,0]v−k+2 = [0,1,0,...0,0]⋮⋮v0 = [0,0,0,,...0,1]vi =vj+vr for all 1≤i≤s with -k+1≤j, r≤i-1vs = [n0,...,nk-1]w = (w1,...ws), wi=(j,r). For example, a vectorial addition chain for [22,18,3] is V=([1,0,0],[0,1,0],[0,0,1],[1,1,0],[2,2,0],[4,4,0],[5,4,0],[10,8,0],[11,9,0],[11,9,1],[22,18,2],[22,18,3])w=((-2,-1),(1,1),(2,2),(-2,3),(4,4),(1,5),(0,6),(7,7),(0,8))

Property Value
dbo:abstract
  • In mathematics, for positive integers k and s, a vectorial addition chain is a sequence V of k-dimensional vectors of nonnegative integers vi for −k + 1 ≤ i ≤ s together with a sequence w,such that v−k+1 = [1,0,0,...0,0]v−k+2 = [0,1,0,...0,0]⋮⋮v0 = [0,0,0,,...0,1]vi =vj+vr for all 1≤i≤s with -k+1≤j, r≤i-1vs = [n0,...,nk-1]w = (w1,...ws), wi=(j,r). For example, a vectorial addition chain for [22,18,3] is V=([1,0,0],[0,1,0],[0,0,1],[1,1,0],[2,2,0],[4,4,0],[5,4,0],[10,8,0],[11,9,0],[11,9,1],[22,18,2],[22,18,3])w=((-2,-1),(1,1),(2,2),(-2,3),(4,4),(1,5),(0,6),(7,7),(0,8)) Vectorial addition chains are well suited to perform multi-exponentiation: Input: Elements x0,...,xk-1 of an abelian group G and a vectorial addition chain of dimension k computing [n0,...,nk-1]Output:The element x0n0...xk-1nr-1 1. * for i =-k+1 to 0 do yi → xi+k-1 2. * for i = 1 to s do yi →yj×yr 3. * return ys (en)
dbo:wikiPageID
  • 21139664 (xsd:integer)
dbo:wikiPageLength
  • 2519 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1024809967 (xsd:integer)
dbo:wikiPageWikiLink
dbp:wikiPageUsesTemplate
dct:subject
rdf:type
rdfs:comment
  • In mathematics, for positive integers k and s, a vectorial addition chain is a sequence V of k-dimensional vectors of nonnegative integers vi for −k + 1 ≤ i ≤ s together with a sequence w,such that v−k+1 = [1,0,0,...0,0]v−k+2 = [0,1,0,...0,0]⋮⋮v0 = [0,0,0,,...0,1]vi =vj+vr for all 1≤i≤s with -k+1≤j, r≤i-1vs = [n0,...,nk-1]w = (w1,...ws), wi=(j,r). For example, a vectorial addition chain for [22,18,3] is V=([1,0,0],[0,1,0],[0,0,1],[1,1,0],[2,2,0],[4,4,0],[5,4,0],[10,8,0],[11,9,0],[11,9,1],[22,18,2],[22,18,3])w=((-2,-1),(1,1),(2,2),(-2,3),(4,4),(1,5),(0,6),(7,7),(0,8)) (en)
rdfs:label
  • Vectorial addition chain (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageWikiLink of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License
  NODES