New Algorithms for Generating Conway Polynomials over Finite Fields

dc.contributor.authorHeath, Lenwood S.en
dc.contributor.authorLoehr, Nicholas A.en
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2013-06-19T14:35:39Zen
dc.date.available2013-06-19T14:35:39Zen
dc.date.issued1998-07-01en
dc.description.abstractArithmetic in a finite field of prime characteristic p normally employs an irreducible polynomial in Z_p[X]. A particular class of irreducible polynomials, generally known as Conway polynomials, provides a means for representing several finite fields of characteristic p in a compatible manner. Conway polynomials are used in computational algebra systems such as GAP and Magma to represent finite fields. The generation of the Conway polynomials for a particular finite field has previously been done by an often expensive brute force search. As a consequence, only a few Conway polynomials have been generated. We present two algorithms for generating Conway polynomials that avoid the brute force search. We have implemented one of these algorithms in Magma and present numerous new Conway polynomials that implementation generated.en
dc.format.mimetypeapplication/postscripten
dc.identifierhttp://eprints.cs.vt.edu/archive/00000493/en
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00000493/01/TR-98-14.psen
dc.identifier.trnumberTR-98-14en
dc.identifier.urihttp://hdl.handle.net/10919/20003en
dc.language.isoenen
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen
dc.relation.ispartofHistorical Collection(Till Dec 2001)en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.titleNew Algorithms for Generating Conway Polynomials over Finite Fieldsen
dc.typeTechnical reporten
dc.type.dcmitypeTexten

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