Index calculus with double large prime variation for curves of small genus with cyclic class group
| dc.creator | Diem, Claus | |
| dc.date | 2006-06-23 | |
| dc.date.accessioned | 2026-07-07T07:17:38Z | |
| dc.date.available | 2026-07-07T07:17:38Z | |
| dc.description | We present an index calculus algorithm with double large prime variation which lends itself well to a rigorous analysis. Using this algorithm we prove that for fixed genus $g \geq 2$, the discrete logarithm problem in degree 0 class groups of non-singular curves over finite fields $\mathbb{F}_q$ can be solved in an expected time of $\tilde{O}(q^{2-2/g})$, provided that the curve is given by a plane model of bounded degree and the degree 0 class group is cyclic. The result generalizes a previous result for hyperelliptic curves given by an imaginary Weierstraß equation obtained by Gaudry, Thomé, Thériault and the author. | |
| dc.identifier | https://arxiv.org/abs/math/0606607 | |
| dc.identifier | http://arxiv.org/abs/math/0606607 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/114009 | |
| dc.subject | Number Theory | |
| dc.subject | 11Y16; 14G50 | |
| dc.title | Index calculus with double large prime variation for curves of small genus with cyclic class group | |
| dc.type | text |