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• W2883353888 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." @default.
• W2883353888 created "2018-08-03" @default.
• W2883353888 creator A5020091226 @default.
• W2883353888 creator A5066894707 @default.
• W2883353888 date "2018-07-13" @default.
• W2883353888 modified "2023-09-27" @default.
• W2883353888 title "Curves, Jacobians, and Cryptography" @default.
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• W2883353888 hasPublicationYear "2018" @default.
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