Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2 = x5 + ax
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Using Abelian Varieties to Improve Pairing-Based Cryptography
Journal of Cryptology
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
Abelian varieties with prescribed embedding degree
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
Constructing pairing-friendly genus 2 curves with ordinary Jacobians
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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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 ⊂ P3(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.