2005-07-01Buch DOI: 10.18452/2570
Reduktions- und Additionsverfahren für die Jacobische Varietät von Kurvenfamilien mit kryptischen Anwendungen
 dc.contributor.author Petkova, Maria dc.date.accessioned 2017-06-15T17:35:15Z dc.date.available 2017-06-15T17:35:15Z dc.date.created 2005-11-02 dc.date.issued 2005-07-01 dc.identifier.issn 0863-0976 dc.identifier.uri http://edoc.hu-berlin.de/18452/3222 dc.description.abstract In 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.iso ger dc.publisher Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ dc.subject Jacobian Varieties eng dc.subject Non hyperelliptic curves of genus 3 eng dc.subject Addition Law eng dc.subject.ddc 510 Mathematik dc.title Reduktions- und Additionsverfahren für die Jacobische Varietät von Kurvenfamilien mit kryptischen Anwendungen dc.type book dc.identifier.urn urn:nbn:de:kobv:11-10051901 dc.identifier.doi http://dx.doi.org/10.18452/2570 local.edoc.container-title Preprints aus dem Institut für Mathematik local.edoc.pages 25 local.edoc.type-name Buch local.edoc.container-type series local.edoc.container-type-name Schriftenreihe local.edoc.container-volume 2005 local.edoc.container-issue 14 local.edoc.container-year 2005 local.edoc.container-erstkatid 2075199-0