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Curves, Jacobians, and cryptography (Q5236869)

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scientific article; zbMATH DE number 7117917

Language	Label	Description	Also known as
English	Curves, Jacobians, and cryptography	scientific article; zbMATH DE number 7117917

Statements

scholarly article

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Curves, Jacobians, and cryptography (English)

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Algebraic Curves and Their Applications

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publication date

16 October 2019

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full work available at URL

https://arxiv.org/abs/1807.05270

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zbMATH Keywords

curves

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Jacobians

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cryptography

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abelian varieties

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MaRDI profile type

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Improved complexity bounds for counting points on hyperelliptic curves

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Genus-2 curves and Jacobians with a given number of points

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Modular Polynomials for Genus 2

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Constructing elliptic curve isogenies in quantum subexponential time

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Handbook of Elliptic and Hyperelliptic Curve Cryptography

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Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic

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Explicit isogenies in quadratic time in any characteristic

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Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies

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The irreducibility of the space of curves of a given genus

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Les Schémas de Modules de Courbes Elliptiques

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New directions in cryptography

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The arithmetic-geometric mean and isogenies for curves of higher genus

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A general framework for subexponential discrete logarithm algorithms

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Fast addition on non-hyperelliptic genus 3 curves

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Isogenies in Theory and Praxis

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Correspondences on Hyperelliptic Curves and Applications to the Discrete Logarithm

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Normal forms of hyperelliptic curves of genus 3

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Fast genus 2 arithmetic based on Theta functions

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Constructive and destructive facets of Weil descent on elliptic curves

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Counting Points on Genus 2 Curves with Real Multiplication

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Modular equations for hyperelliptic curves

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A double large prime variation for small genus hyperelliptic index calculus

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The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines

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Genus 2 point counting over prime fields

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Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two

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Computing Riemann-Roch spaces in algebraic function fields and related topics.

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Arithmetic variety of moduli for genus two

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On Siegel Modular Forms of Genus Two

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The Past, Evolving Present, and Future of the Discrete Logarithm

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Division polynomials and multiplication formulae of Jacobian varieties of dimension 2

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Corrections to “Division polynomials and multiplication formulae in dimension 2”

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Arithmetic Moduli of Elliptic Curves. (AM-108)

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Serre's modularity conjecture. II

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Modularity of 2-adic Barsotti-Tate representations

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A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem

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About the group law for the Jacobi variety of a hyperelliptic curve

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Computing the geometric endomorphism ring of a genus-2 Jacobian

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Computing isogenies between abelian varieties

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Computing separable isogenies in quasi-optimal time

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A universal genus-two curve from Siegel modular forms

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Modular curves and the Eisenstein ideal

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DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS

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New lattice-based cryptographic constructions

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On the generic curve of genus 3

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Computing low-degree isogenies in genus 2 with the Dolgachev–Lehavi method

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Algebraic Function Fields and Codes

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Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves

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Endomorphisms of Abelian varieties over finite fields

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2-dimensional simple factors of \(J_ 0(N)\)

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Hyperelliptic Simple Factors of J<sub>0</sub>(N) with Dimension at Least 3

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Constructing hyperelliptic curves of genus 2 suitable for cryptography

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Families of absolutely simple hyperelliptic jacobians

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Identifiers

zbMATH Open document ID

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Mathematics Subject Classification ID

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zbMATH DE Number

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10.1090/CONM/724/14596

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Sitelinks

Mathematics(1 entry)

mardi Publication:5236869

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