Name
Abstract | ||
|---|---|---|
We show how to compute the pre-images of multiplication-by-2 in Jacobians of genus 2 curves C : y 2 = f ( x ) over F q with q odd. We characterize D = u ( x ) , v ( x ) ¿ 2 Jac ( C ) ( F q ) in terms of the quadratic character of u ( x ) at the roots of f ( x ) in imaginary models, and in terms of the quadratic character of the quotients of u ( x ) at pairs of roots of f ( x ) in real models. Our method reduces the problem to the computation of at most 5 square roots over the splitting field of f ( x ) plus the solution of a system of linear equations. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.ffa.2015.08.001 | Finite Fields and Their Applications |
Keywords | Field | DocType |
11G20,11T71,14G50,14H40,14H45 | Combinatorics,System of linear equations,Algebra,Splitting field,Bisection,Quotient,Quadratic equation,Square root,Mathematics,Computation | Journal |
Volume | Issue | ISSN |
36 | C | 1071-5797 |
Citations | PageRank | References |
0 | 0.34 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Josep M. Miret | 1 | 81 | 14.88 |
| Jordi Pujolàs | 2 | 24 | 5.98 |
| Nicolas Thériault | 3 | 177 | 13.06 |