Fast heuristic algorithms for computing relations in the class group of a quadratic order, with applications to isogeny evaluation

DOI10.1112/S1461157016000358zbMath1391.11160MaRDI QIDQ2971023

Claus Fieker, Jean-François Biasse, Michael J. Jacobson jun.

Publication date: 4 April 2017

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

Mathematics Subject Classification ID

Quadratic extensions (11R11) Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Isogeny (14K02)

Related Items (3)

A proof of the conjectured run time of the Hafner-McCurley class group algorithm ⋮ Computational problems in supersingular elliptic curve isogenies ⋮ Quantum security analysis of CSIDH

Cites Work

• Expander graphs based on GRH with an application to elliptic curve cryptography
• Counting points on elliptic curves over finite fields
• Computing the endomorphism ring of an ordinary elliptic curve over a finite field
• Computing residue class rings and Picard groups of orders
• On the quaternion -isogeny path problem
• Computing endomorphism rings of elliptic curves under the GRH
• A Subexponential Algorithm for Evaluating Large Degree Isogenies
• A sieve algorithm for the shortest lattice vector problem
• Modular polynomials via isogeny volcanoes
• Constructing elliptic curve isogenies in quantum subexponential time

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