A CRT algorithm for constructing genus 2 curves over finite fields
| dc.creator | Eisentraeger, Kirsten | |
| dc.creator | Lauter, Kristin | |
| dc.date | 2004-05-15 | |
| dc.date | 2007-01-11 | |
| dc.date.accessioned | 2026-07-07T07:39:39Z | |
| dc.date.available | 2026-07-07T07:39:39Z | |
| dc.description | We present a new method for constructing genus 2 curves over a finite field with a given number of points on its Jacobian. This method has important applications in cryptography, where groups of prime order are used as the basis for discrete-log based cryptosystems. Our algorithm provides an alternative to the traditional CM method for constructing genus 2 curves. For a quartic CM field K with primitive CM type, we compute the Igusa class polynomials modulo p for certain small primes p and then use the Chinese remainder theorem (CRT) and a bound on the denominators to construct the class polynomials. We also provide an algorithm for determining endomorphism rings of ordinary Jacobians of genus 2 curves over finite fields, generalizing the work of Kohel for elliptic curves. | |
| dc.description | 16 pages. to appear in Proceedings of AGCT-10 | |
| dc.identifier | https://arxiv.org/abs/math/0405305 | |
| dc.identifier | http://arxiv.org/abs/math/0405305 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121528 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G15; 11G10; 11R37; 14G50 | |
| dc.title | A CRT algorithm for constructing genus 2 curves over finite fields | |
| dc.type | text |