Computing discrete logarithms in real quadratic congruence function fields of large genus

DOI10.1090/S0025-5718-99-01040-6zbMath1036.11064OpenAlexW2001149042MaRDI QIDQ4235520

Volker Müller, Christoph Thiel, Andreas Stein

Publication date: 22 March 1999

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01040-6

zbMATH Keywords

class groupprobabilistic algorithmsubexponential algorithmDiscrete logarithmreal quadratic congruence function field

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cryptography (94A60) Data encryption (aspects in computer science) (68P25) Number-theoretic algorithms; complexity (11Y16) Cyclotomic function fields (class groups, Bernoulli objects, etc.) (11R60)

Related Items (17)

Smooth ideals in hyperelliptic function fields ⋮ A review on the isomorphism classes of hyperelliptic curves of genus 2 over finite fields admitting a Weierstrass point ⋮ The arithmetic of Jacobian groups of superelliptic cubics ⋮ Equivalences between elliptic curves and real quadratic congruence function fields ⋮ An \(L(1/3)\) discrete logarithm algorithm for low degree curves ⋮ The index calculus method using non-smooth polynomials ⋮ Arithmetic on superelliptic curves ⋮ Computing discrete logarithms in high-genus hyperelliptic Jacobians in provably subexponential time ⋮ Explicit bounds and heuristics on class numbers in hyperelliptic function fields ⋮ Sieving in Function Fields ⋮ Cryptographic aspects of real hyperelliptic curves ⋮ Linearizing torsion classes in the Picard group of algebraic curves over finite fields ⋮ The infrastructure of a global field of arbitrary unit rank ⋮ Decision problems in quadratic function fields of high genus ⋮ A double large prime variation for small genus hyperelliptic index calculus ⋮ Constructive and destructive facets of Weil descent on elliptic curves ⋮ Computing discrete logarithms in the Jacobian of high-genus hyperelliptic curves over even characteristic finite fields

Cites Work

• Algebraic function fields and codes
• Key-exchange in real quadratic congruence function fields
• Lectures on the theory of algebraic functions of one variable
• Der Primdivisorsatz für algebraische Funktionenkörper über einem endlichen Konstantenkörper
• Hermite Normal Form Computation Using Modulo Determinant Arithmetic
• Explicit Bounds for Primality Testing and Related Problems
• Some Methods for Evaluating the Regulator of a Real Quadratic Function Field
• Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve
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