Heuristics on pairing-friendly abelian varieties

DOI10.1112/S1461157015000091zbMath1397.11113arXiv1202.1177MaRDI QIDQ2942134

David Gruenewald, John L. Boxall

Publication date: 26 August 2015

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

Full work available at URL: https://arxiv.org/abs/1202.1177

zbMATH Keywords

isogeny classesembedding degreepairing-friendly abelian varieties

Mathematics Subject Classification ID

Arithmetic ground fields for abelian varieties (14K15) Varieties over finite and local fields (11G25)

Cites Work

• Unnamed Item
• Elliptic curves with low embedding degree
• Using abelian varieties to improve pairing-based cryptography
• The improbability that an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm
• The Magma algebra system. I: The user language
• Generating pairing-friendly parameters for the CM construction of genus 2 curves over prime fields
• A taxonomy of pairing-friendly elliptic curves
• Heuristics of the Cocks-Pinch method
• Ordinary Abelian varieties having small embedding degree
• Endomorphisms of Abelian varieties over finite fields
• Isogeny classes of abelian varieties over finite fields
• Elliptic curves suitable for pairing based cryptography
• Abelian Varieties with Prescribed Embedding Degree
• A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
• The Distribution of Galois Groups and Hilbert's Irreducibility Theorem
• Heuristics on pairing-friendly elliptic curves
• Class Invariants by the CRT Method
• On the number of isogeny classes of pairing-friendly elliptic curves and statistics of MNT curves
• Pairing-Friendly Elliptic Curves of Prime Order
• Abelian varieties over finite fields