Counting hyperelliptic curves that admit a Koblitz model
| dc.creator | Demirkiran, Cevahir | |
| dc.creator | Nart, Enric | |
| dc.date | 2007-05-10 | |
| dc.date.accessioned | 2026-07-07T08:00:37Z | |
| dc.date.available | 2026-07-07T08:00:37Z | |
| dc.description | Let k be a finite field of odd characteristic. We find a closed formula for the number of k-isomorphism classes of pointed, and non-pointed, hyperelliptic curves of genus g over k, admitting a Koblitz model. These numbers are expressed as a polynomial in the cardinality q of k, with integer coefficients (for pointed curves) and rational coefficients (for non-pointed curves). The coefficients depend on g and the set of divisors of q-1 and q+1. These formulas show that the number of hyperelliptic curves of genus g suitable (in principle) of cryptographic applications is asymptotically (1-e^{-1})2q^{2g-1}, and not 2q^{2g-1} as it was believed. The curves of genus g=2 and g=3 are more resistant to the attacks to the DLP; for these values of g the number of curves is respectively (91/72)q^3+O(q^2) and (3641/2880)q^5+O(q^4). | |
| dc.identifier | https://arxiv.org/abs/0705.1423 | |
| dc.identifier | http://arxiv.org/abs/0705.1423 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128709 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11G20 | |
| dc.title | Counting hyperelliptic curves that admit a Koblitz model | |
| dc.type | text |