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2005-07-01Buch DOI: 10.18452/2570
Reduktions- und Additionsverfahren für die Jacobische Varietät von Kurvenfamilien mit kryptischen Anwendungen
dc.contributor.authorPetkova, Maria
dc.date.accessioned2017-06-15T17:35:15Z
dc.date.available2017-06-15T17:35:15Z
dc.date.created2005-11-02
dc.date.issued2005-07-01
dc.identifier.issn0863-0976
dc.identifier.urihttp://edoc.hu-berlin.de/18452/3222
dc.description.abstractIn this paper we represent a reduction and addition algorithm for non hyperelliptic curves of genus 3. Our aim is to give an explicit representation of the group law in the jacobian varieties of curves belonging to the families $y^4=p_4(x)$ and $y^4=p_3(x)$. The idea of the algorithm is an extension of the geometric addition of points on elliptic curves. Because of the complexity of the curve structure we work hier with conics instead of chords and tangents as in the genus one case. In the construction of the algorithm we use the so called coordinate form of the divisor. The coordinate form of a divisor is a unique set of three polynomials, which we use for the computations. All computations succeed only with linear algebra knowledges. At the end of the algorithm we need one factorisation so that the result can be defined over a finite extension field. The reduction and addition ist constructed iterativ and can be applied in efficient way to divisors of every degree.eng
dc.language.isoger
dc.publisherHumboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectJacobian Varietieseng
dc.subjectNon hyperelliptic curves of genus 3eng
dc.subjectAddition Laweng
dc.subject.ddc510 Mathematik
dc.titleReduktions- und Additionsverfahren für die Jacobische Varietät von Kurvenfamilien mit kryptischen Anwendungen
dc.typebook
dc.identifier.urnurn:nbn:de:kobv:11-10051901
dc.identifier.doihttp://dx.doi.org/10.18452/2570
local.edoc.container-titlePreprints aus dem Institut für Mathematik
local.edoc.pages25
local.edoc.type-nameBuch
local.edoc.container-typeseries
local.edoc.container-type-nameSchriftenreihe
local.edoc.container-volume2005
local.edoc.container-issue14
local.edoc.container-year2005
local.edoc.container-erstkatid2075199-0

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