2010 | OriginalPaper | Buchkapitel
A New Method for Constructing Pairing-Friendly Abelian Surfaces
verfasst von : Robert Dryło
Erschienen in: Pairing-Based Cryptography - Pairing 2010
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We present a new method for constructing simple ordinary abelian surfaces with a small embedding degree. To a quartic CM field
K
, we associate a quadric surface
H
⊂ ℙ
3
(ℚ) and use its parametrization to determine Weil numbers in
K
corresponding in the sense of Honda-Tate theory to such surfaces. In general, the resulting surfaces have parameter
ρ
≈ 8. However, if there exist rational lines on
H
, they can be used to achieve
ρ
≈ 4. We give examples of non-primitive quartic CM fields such that
H
has rulings by rational lines. Furthermore, we show how our method can be used to construct parametric families of pairing-friendly surfaces.