Curves, Jacobians, and cryptography
| Autor: | Gerhard Frey, Tony Shaska |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
business.industry
Cryptography Galois module Algebra Mathematics - Algebraic Geometry symbols.namesake Mathematics::Algebraic Geometry Genus (mathematics) Mathematik Jacobian matrix and determinant FOS: Mathematics symbols Torsion (algebra) Abelian group Elliptic curve cryptography business Algebraic Geometry (math.AG) Key exchange Computer Science::Cryptography and Security Mathematics |
| Zdroj: | Algebraic Curves and Their Applications. :279-344 |
| ISSN: | 1098-3627 0271-4132 |
| Popis: | The main purpose of this paper is to give an overview over the theory of abelian varieties, with main focus on Jacobian varieties of curves reaching from well-known results till to latest developments and their usage in cryptography. In the first part we provide the necessary mathematical background on abelian varieties, their torsion points, Honda-Tate theory, Galois representations, with emphasis on Jacobian varieties and hyperelliptic Jacobians. In the second part we focus on applications of abelian varieties on cryptography and treating separately, elliptic curve cryptography, genus 2 and 3 cryptography, including Diffie-Hellman Key Exchange, index calculus in Picard groups, isogenies of Jacobians via correspondences and applications to discrete logarithms. Several open problems and new directions are suggested. 66 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|