Matches in SemOpenAlex for { <https://semopenalex.org/work/W4295269968> ?p ?o ?g. }
Showing items 1 to 81 of
81
with 100 items per page.
- W4295269968 abstract "Constructing $r$-th nonresidue over a finite field is a fundamental computational problem. A related problem is to construct an irreducible polynomial of degree $r^e$ (where $r$ is a prime) over a given finite field $mathbb{F}_q$ of characteristic $p$ (equivalently, constructing the bigger field $mathbb{F}_{q^{r^e}}$). Both these problems have famous randomized algorithms but the derandomization is an open question. We give some new connections between these two problems and their variants. In 1897, Stickelberger proved that if a polynomial has an odd number of even degree factors, then its discriminant is a quadratic nonresidue in the field. We give an extension of Stickelberger's Lemma; we construct $r$-th nonresidues from a polynomial $f$ for which there is a $d$, such that, $r|d$ and $rnmid,$#(irreducible factor of $f(x)$ of degree $d$). Our theorem has the following interesting consequences: (1) we can construct $mathbb{F}_{q^m}$ in deterministic poly(deg($f$),$mlog q$)-time if $m$ is an $r$-power and $f$ is known; (2) we can find $r$-th roots in $mathbb{F}_{p^m}$ in deterministic poly($mlog p$)-time if $r$ is constant and $r|gcd(m,p-1)$. We also discuss a conjecture significantly weaker than the Generalized Riemann hypothesis to get a deterministic poly-time algorithm for $r$-th root finding." @default.
- W4295269968 created "2022-09-12" @default.
- W4295269968 creator A5050912226 @default.
- W4295269968 creator A5068244186 @default.
- W4295269968 creator A5072953772 @default.
- W4295269968 creator A5084229662 @default.
- W4295269968 date "2017-02-02" @default.
- W4295269968 modified "2023-09-25" @default.
- W4295269968 title "Irreducibility and r-th root finding over finite fields" @default.
- W4295269968 doi "https://doi.org/10.48550/arxiv.1702.00558" @default.
- W4295269968 hasPublicationYear "2017" @default.
- W4295269968 type Work @default.
- W4295269968 citedByCount "0" @default.
- W4295269968 crossrefType "posted-content" @default.
- W4295269968 hasAuthorship W4295269968A5050912226 @default.
- W4295269968 hasAuthorship W4295269968A5068244186 @default.
- W4295269968 hasAuthorship W4295269968A5072953772 @default.
- W4295269968 hasAuthorship W4295269968A5084229662 @default.
- W4295269968 hasBestOaLocation W42952699681 @default.
- W4295269968 hasConcept C101044782 @default.
- W4295269968 hasConcept C114614502 @default.
- W4295269968 hasConcept C118615104 @default.
- W4295269968 hasConcept C121332964 @default.
- W4295269968 hasConcept C134306372 @default.
- W4295269968 hasConcept C154945302 @default.
- W4295269968 hasConcept C165030954 @default.
- W4295269968 hasConcept C184992742 @default.
- W4295269968 hasConcept C18903297 @default.
- W4295269968 hasConcept C202444582 @default.
- W4295269968 hasConcept C24890656 @default.
- W4295269968 hasConcept C2775997480 @default.
- W4295269968 hasConcept C2776823524 @default.
- W4295269968 hasConcept C2777759810 @default.
- W4295269968 hasConcept C2780990831 @default.
- W4295269968 hasConcept C33923547 @default.
- W4295269968 hasConcept C41008148 @default.
- W4295269968 hasConcept C46757340 @default.
- W4295269968 hasConcept C77926391 @default.
- W4295269968 hasConcept C78397625 @default.
- W4295269968 hasConcept C86803240 @default.
- W4295269968 hasConcept C90119067 @default.
- W4295269968 hasConcept C9652623 @default.
- W4295269968 hasConceptScore W4295269968C101044782 @default.
- W4295269968 hasConceptScore W4295269968C114614502 @default.
- W4295269968 hasConceptScore W4295269968C118615104 @default.
- W4295269968 hasConceptScore W4295269968C121332964 @default.
- W4295269968 hasConceptScore W4295269968C134306372 @default.
- W4295269968 hasConceptScore W4295269968C154945302 @default.
- W4295269968 hasConceptScore W4295269968C165030954 @default.
- W4295269968 hasConceptScore W4295269968C184992742 @default.
- W4295269968 hasConceptScore W4295269968C18903297 @default.
- W4295269968 hasConceptScore W4295269968C202444582 @default.
- W4295269968 hasConceptScore W4295269968C24890656 @default.
- W4295269968 hasConceptScore W4295269968C2775997480 @default.
- W4295269968 hasConceptScore W4295269968C2776823524 @default.
- W4295269968 hasConceptScore W4295269968C2777759810 @default.
- W4295269968 hasConceptScore W4295269968C2780990831 @default.
- W4295269968 hasConceptScore W4295269968C33923547 @default.
- W4295269968 hasConceptScore W4295269968C41008148 @default.
- W4295269968 hasConceptScore W4295269968C46757340 @default.
- W4295269968 hasConceptScore W4295269968C77926391 @default.
- W4295269968 hasConceptScore W4295269968C78397625 @default.
- W4295269968 hasConceptScore W4295269968C86803240 @default.
- W4295269968 hasConceptScore W4295269968C90119067 @default.
- W4295269968 hasConceptScore W4295269968C9652623 @default.
- W4295269968 hasLocation W42952699681 @default.
- W4295269968 hasOpenAccess W4295269968 @default.
- W4295269968 hasPrimaryLocation W42952699681 @default.
- W4295269968 hasRelatedWork W1995459792 @default.
- W4295269968 hasRelatedWork W2160995578 @default.
- W4295269968 hasRelatedWork W2168517325 @default.
- W4295269968 hasRelatedWork W2280910813 @default.
- W4295269968 hasRelatedWork W2587171926 @default.
- W4295269968 hasRelatedWork W2962782598 @default.
- W4295269968 hasRelatedWork W2964996896 @default.
- W4295269968 hasRelatedWork W3089650418 @default.
- W4295269968 hasRelatedWork W3127231709 @default.
- W4295269968 hasRelatedWork W4295269968 @default.
- W4295269968 isParatext "false" @default.
- W4295269968 isRetracted "false" @default.
- W4295269968 workType "article" @default.