Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time

DOI10.1090/S0025-5718-01-01363-1zbMath0988.68069WikidataQ56337877 ScholiaQ56337877MaRDI QIDQ2781220

Andreas Enge

Publication date: 19 March 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

hyperelliptic curveJacobiandiscrete logarithmsubexponentiality

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Data encryption (aspects in computer science) (68P25) Number-theoretic algorithms; complexity (11Y16) Jacobians, Prym varieties (14H40) Computational aspects of algebraic curves (14Q05) Arithmetic ground fields for abelian varieties (14K15) Varieties over finite and local fields (11G25)

Related Items (18)

A simple method for obtaining relations among factor basis elements for special hyperelliptic curves ⋮ Fast cryptography in genus 2 ⋮ Sublinear Scalar Multiplication on Hyperelliptic Koblitz Curves ⋮ A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point ⋮ Isomorphism classes of hyperelliptic curves of genus 2 over finite fields with characteristic 2 ⋮ The arithmetic of Jacobian groups of superelliptic cubics ⋮ Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with even characteristic ⋮ Index calculus in the trace zero variety ⋮ Index calculus algorithm for non-planar curves ⋮ An \(L(1/3)\) discrete logarithm algorithm for low degree curves ⋮ Rethinking low genus hyperelliptic Jacobian arithmetic over binary fields: interplay of field arithmetic and explicit formulæ ⋮ Counting isomorphism classes of pointed hyperelliptic curves of genus 4 over finite fields with odd characteristic ⋮ A new method for decomposition in the Jacobian of small genus hyperelliptic curves ⋮ An 𝐿(1/3) algorithm for ideal class group and regulator computation in certain number fields ⋮ Isomorphism classes of hyperelliptic curves of genus 3 over finite fields ⋮ A generic approach to searching for Jacobians ⋮ Super-Isolated Elliptic Curves and Abelian Surfaces in Cryptography ⋮ A double large prime variation for small genus hyperelliptic index calculus

Cites Work

• Hyperelliptic cryptosystems
• Algorithmic number theory. 1st international symposium, ANTS-I, Ithaca, NY, USA, May 6-9, 1994. Proceedings
• Counting points on curves over finite fields
• Algorithmic number theory. Second international symposium, ANTS-II, Talence, France, May 18-23, 1996. Proceedings
• Hermite Normal Form Computation Using Modulo Determinant Arithmetic
• Computing in the Jacobian of a Hyperelliptic Curve
• Computing discrete logarithms in real quadratic congruence function fields of large genus
• Smooth ideals in hyperelliptic function fields
• Sieving in Function Fields
• Frobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields
• Algebraic aspects of cryptography. With an appendix on hyperelliptic curves by Alfred J. Menezes, Yi-Hong Wu, and Robert J. Zuccherato
• The extended Euclidean algorithm on polynomials, and the computational efficiency of hyperelliptic cryptosystems
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