Name
Abstract | ||
|---|---|---|
By reversing reduction in divisor class arithmetic we provide efficient trisection algorithms for supersingular Jacobians of genus 2 curves over finite fields of characteristic 2. With our technique we obtain new results for these Jacobians: we show how to find their 3-torsion subgroup, we prove there is none with 3-torsion subgroup of rank 3 and we prove that the maximal 3-power order subgroup is isomorphic to either Z/3(nu)Z or (Z/3(nu/2)Z)(2) or (Z/3(nu/4)Z)(4), where nu is the 3-adic valuation nu(3)(#Jac(C)(F(2)m)). Ours are the first trisection formulae available in literature. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.3934/amc.2014.8.375 | ADVANCES IN MATHEMATICS OF COMMUNICATIONS |
Keywords | Field | DocType |
Hyperelliptic curve,supersingular,genus 2,divisor class,trisection,binary field,explicit formulas | Discrete mathematics,Hyperelliptic curve,Finite field,Combinatorics,Binary fields,Isomorphism,Divisor,Mathematics | Journal |
Volume | Issue | ISSN |
8 | SP4 | 1930-5346 |
Citations | PageRank | References |
2 | 0.49 | 3 |
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 |