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Horizontal isogeny graphs of ordinary abelian varieties and the discrete logarithm problem
Isogeny expander graph hyperelliptic curve cryptography
2017/2/20
Fix an ordinary abelian variety defined over a finite field. The ideal class group of its endomorphism ring acts freely on the set of isogenous varieties with same endomorphism ring, by complex multip...
Isogeny graphs of ordinary abelian varieties
Jacobians of hyperelliptic curves genus 2 cryptography isogeny graphs
2016/12/8
Fix a prime number ГГ. Graphs of isogenies of degree a power of ГГ are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ord...
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Abelian varieties hyperelliptic curves pairing-based cryptosystems
2009/6/3
We give an algorithm that produces families ofWeil numbers
for ordinary abelian varieties over finite fields with prescribed embedding
degree. The algorithm uses the ideas of Freeman, Stevenhagen, a...
Ordinary abelian varieties having small embedding degree
Ordinary abelian varieties small embedding degree MNT
2009/4/3
Miyaji, Nakabayashi and Takano (MNT) gave families of
group orders of ordinary elliptic curves with embedding degree suitable
for pairing applications. In this paper we generalise their results by g...