dc.contributor.advisor Gjøsteen, Kristian nb_NO dc.contributor.author Rasmussen, Lars Lone nb_NO dc.date.accessioned 2014-12-19T13:57:34Z dc.date.available 2014-12-19T13:57:34Z dc.date.created 2010-09-02 nb_NO dc.date.issued 2009 nb_NO dc.identifier 347136 nb_NO dc.identifier ntnudaim:4552 nb_NO dc.identifier.uri http://hdl.handle.net/11250/258253 dc.description.abstract Hyperelliptic curves could be considered against elliptic curves for cryptography by virtue of using smaller fields and therefore being faster, but they have several weaknesses. Index calculus attacks are effective against hyperelliptic curves of higher genus, only $g=2$ is considered safe at the moment. Hyperelliptic curves have more involved group operations, and the potential speed gain is dependent on hardware configurations fully utilizing the small fields. Lastly, hyperelliptic curve cryptography is relatively new and untested. Elliptic curve cryptography has been around for a long time, and there is no compelling argument for switching to hyperelliptic curves. Index calculus attacks on hyperelliptic curves are quite effective compared to general discrete log algorithms for genus higher than 4. However, they are of limited use when applied to hyperelliptic curve cryptosystems, as high genus curves are not used here. Their function is more one of guiding, eliminating curves and fields for use in applications. The Weil descent attack on elliptic curves is again interesting, but not too relevant in practice. The fields for which it is possible are avoided in serious use. Again, the main function of the attack is as a reminder on which fields not to use. nb_NO dc.language eng nb_NO dc.publisher Institutt for matematiske fag nb_NO dc.subject ntnudaim no_NO dc.subject SIF3 fysikk og matematikk no_NO dc.subject Industriell matematikk no_NO dc.title Index Calculus Attacks on Hyperelliptic Curves nb_NO dc.type Master thesis nb_NO dc.source.pagenumber 37 nb_NO dc.contributor.department Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag nb_NO
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