Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves
| dc.creator | Smith, Benjamin | |
| dc.date | 2008-06-18 | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:46:54Z | |
| dc.date.available | 2026-07-07T12:46:54Z | |
| dc.description | We describe the use of explicit isogenies to translate instances of the Discrete Logarithm Problem (DLP) from Jacobians of hyperelliptic genus 3 curves to Jacobians of non-hyperelliptic genus 3 curves, where they are vulnerable to faster index calculus attacks. We provide explicit formulae for isogenies with kernel isomorphic to $(\ZZ/2\ZZ)^3$ (over an algebraic closure of the base field) for any hyperelliptic genus 3 curve over a field of characteristic not 2 or 3. These isogenies are rational for a positive fraction of all hyperelliptic genus 3 curves defined over a finite field of characteristic $p > 3$. Subject to reasonable assumptions, our constructions give an explicit and efficient reduction of instances of the DLP from hyperelliptic to non-hyperelliptic Jacobians for around 18.57% of all hyperelliptic genus 3 curves over a given finite field. We conclude with a discussion on extending these ideas to isogenies with more general kernels. A condensed version of this work appeared in the proceedings of the EUROCRYPT 2008 conference. | |
| dc.description | This is an extended version of work that appeared in the proceedings of the Eurocrypt 2008 conference | |
| dc.identifier | https://arxiv.org/abs/0806.2995 | |
| dc.identifier | http://arxiv.org/abs/0806.2995 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221541 | |
| dc.subject | Number Theory | |
| dc.subject | 11G20 (Primary); 11Y99, 14H40, 14H45, 14G50 (Secondary) | |
| dc.title | Isogenies and the Discrete Logarithm Problem in Jacobians of Genus 3 Hyperelliptic Curves | |
| dc.type | text |