Back to Search
Start Over
On the p-th division polynomial
- Source :
- UPCommons. Portal del coneixement obert de la UPC, Universitat Politècnica de Catalunya (UPC)
- Publication Year :
- 2022
- Publisher :
- Elsevier BV, 2022.
-
Abstract
- By using the relations between supersingular elliptic curves defined over a finite field of characteristic p > 3 and the p-th division polynomial, we present a property about the reduction modulo a prime p > 3 of the p-th division polynomial based on a heuristic argument and numerical evidence. We prove this property determining the p-th division polynomial of supersingular elliptic curves. As a consequence of this result, we present a criterion to discard supersingular elliptic curves.
- Subjects :
- Polynomial
Algebra and Number Theory
Reduction (recursion theory)
Corbes el·líptiques
Mathematics::Number Theory
Modulo
Nombres, Teoria dels
Division (mathematics)
Polynomials
Supersingular elliptic curve
Curves, Elliptic
Prime (order theory)
Combinatorics
Finite field
Number theory
Polinomis
Matemàtiques i estadística::Àlgebra::Teoria de nombres [Àrees temàtiques de la UPC]
Heuristic argument
Mathematics
Subjects
Details
- ISSN :
- 0022314X
- Volume :
- 233
- Database :
- OpenAIRE
- Journal :
- Journal of Number Theory
- Accession number :
- edsair.doi.dedup.....f86219bc5f8eba8c54573af4e1b35948