Curves, Jacobians, and cryptography

DOI10.1090/conm/724/14596zbMath1428.14044arXiv1807.05270OpenAlexW2963400772MaRDI QIDQ5236869

Tanush Shaska, Gerhard Frey

Publication date: 16 October 2019

Published in: Algebraic Curves and Their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.05270

zbMATH Keywords

cryptographyabelian varietiescurvesJacobians

Mathematics Subject Classification ID

Cryptography (94A60) Families, moduli of curves (algebraic) (14H10) Special algebraic curves and curves of low genus (14H45)

Related Items (8)

From hyperelliptic to superelliptic curves ⋮ On isogenies among certain abelian surfaces ⋮ Isogenous components of Jacobian surfaces ⋮ Index calculus algorithm for non-planar curves ⋮ Unnamed Item ⋮ On the discriminant of certain quadrinomials ⋮ On hyperelliptic curves of genus 3 ⋮ On automorphisms of algebraic curves

Cites Work

• Genus 2 point counting over prime fields
• Constructing public-key cryptographic schemes based on class group action on a set of isogenous elliptic curves
• Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies
• Normal forms of hyperelliptic curves of genus 3
• The arithmetic of characteristic 2 Kummer surfaces and of elliptic Kummer lines
• Serre's modularity conjecture. II
• Modularity of 2-adic Barsotti-Tate representations
• Modular curves and the Eisenstein ideal
• Constructive and destructive facets of Weil descent on elliptic curves
• Computing Riemann-Roch spaces in algebraic function fields and related topics.
• A universal genus-two curve from Siegel modular forms
• About the group law for the Jacobi variety of a hyperelliptic curve
• 2-dimensional simple factors of \(J_ 0(N)\)
• Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two
• Improved complexity bounds for counting points on hyperelliptic curves
• Fast algorithms for computing isogenies between ordinary elliptic curves in small characteristic
• Endomorphisms of Abelian varieties over finite fields
• The irreducibility of the space of curves of a given genus
• Arithmetic variety of moduli for genus two
• A general framework for subexponential discrete logarithm algorithms
• Correspondences on Hyperelliptic Curves and Applications to the Discrete Logarithm
• Explicit isogenies in quadratic time in any characteristic
• Modular Polynomials for Genus 2
• Counting Points on Genus 2 Curves with Real Multiplication
• Computing isogenies between abelian varieties
• Division polynomials and multiplication formulae of Jacobian varieties of dimension 2
• A double large prime variation for small genus hyperelliptic index calculus
• DETERMINANT EXPRESSIONS FOR HYPERELLIPTIC FUNCTIONS
• Algebraic Function Fields and Codes
• Fast addition on non-hyperelliptic genus 3 curves
• Corrections to “Division polynomials and multiplication formulae in dimension 2”
• Arithmetic Moduli of Elliptic Curves. (AM-108)
• New directions in cryptography
• Computing the geometric endomorphism ring of a genus-2 Jacobian
• On the generic curve of genus 3
• Les Schémas de Modules de Courbes Elliptiques
• Constructing hyperelliptic curves of genus 2 suitable for cryptography
• Modular equations for hyperelliptic curves
• The arithmetic-geometric mean and isogenies for curves of higher genus
• Genus-2 curves and Jacobians with a given number of points
• Computing separable isogenies in quasi-optimal time
• The Past, Evolving Present, and Future of the Discrete Logarithm
• Isogenies in Theory and Praxis
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• On Siegel Modular Forms of Genus Two
• Constructing elliptic curve isogenies in quantum subexponential time
• New lattice-based cryptographic constructions
• Fast genus 2 arithmetic based on Theta functions
• Computing low-degree isogenies in genus 2 with the Dolgachev–Lehavi method
• A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
• Hyperelliptic Simple Factors of J₀(N) with Dimension at Least 3
• Families of absolutely simple hyperelliptic jacobians
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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