Real and imaginary quadratic representations of hyperelliptic function fields

DOI10.1090/S0025-5718-99-01066-2zbMath0923.11160MaRDI QIDQ4240591

Sachar Paulus, Hans-Georg Rück

Publication date: 28 April 1999

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

zbMATH Keywords

group lawdivisor class groupimaginary quadratic function fieldreduced idealshyperelliptic function fieldsreal quadratic function field

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Computational aspects of algebraic curves (14Q05) Class groups and Picard groups of orders (11R65) Algebraic functions and function fields in algebraic geometry (14H05)

Related Items (16)

Reducible Abelian varieties and Lax matrices for Euler’s problem of two fixed centres ⋮ Smooth ideals in hyperelliptic function fields ⋮ On the torsion of the Jacobians of the hyperelliptic curves $y^{2}=x^{n}+a$ and $y^{2}=x(x^{n}+a)$ ⋮ Unnamed Item ⋮ Analysis of the GHS Weil Descent Attack on the ECDLP over Characteristic Two Finite Fields of Composite Degree ⋮ Fast Jacobian arithmetic for hyperelliptic curves of genus 3 ⋮ Arithmetic on superelliptic curves ⋮ Algebraic curves and cryptography ⋮ The parallelized Pollard kangaroo method in real quadratic function fields ⋮ Explicit bounds and heuristics on class numbers in hyperelliptic function fields ⋮ Sieving in Function Fields ⋮ Cryptographic aspects of real hyperelliptic curves ⋮ Bisection and squares in genus 2 ⋮ The infrastructure of a global field of arbitrary unit rank ⋮ On the complexity of the discrete logarithm and Diffie-Hellman problems ⋮ A type of hyperelliptic continued fraction

Cites Work

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• Algebraic function fields and codes
• Equivalences between elliptic curves and real quadratic congruence function fields
• Key-exchange in real quadratic congruence function fields
• Computing in the Jacobian of a Hyperelliptic Curve
• Multiples of Points on Elliptic Curves and Continued Fractions

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