Curves, Jacobians, and cryptography

Frey, Gerhard and Shaska, Tanush (2018) Curves, Jacobians, and cryptography. In: Algebraic curves and their applications. Contemporary Mathematics, 724 . American Mathematical Society, USA, pp. 290-357. (In Press)

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Abstract

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.

Item Type: Book Section
Subjects: Q Science >
Divisions: Engineering, Science and Mathematics
Depositing User: Editor Risat
Date Deposited: 09 Apr 2018 16:40
Last Modified: 03 Oct 2018 01:53
URI: http://repo.risat.org/id/eprint/321

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