Examples of genus two CM curves defined over the rationals
Mathematics of Computation
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
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
Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
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
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
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
On the minimal embedding field
Pairing'07 Proceedings of the First 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
A new method for constructing pairing-friendly abelian surfaces
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Generating more Kawazoe-Takahashi genus 2 pairing-friendly hyperelliptic curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Faster pairing computations on curves with high-degree twists
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Avoiding full extension field arithmetic in pairing computations
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
Generating pairing-friendly parameters for the CM construction of genus 2 curves over prime fields
Designs, Codes and Cryptography
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We give an algorithm that produces families of Weil numbers for ordinary abelian varieties over finite fields with prescribed embedding degree. The algorithm uses the ideas of Freeman, Stevenhagen, and Streng to generalize the Brezing-Weng construction of pairing-friendly elliptic curves. We use our algorithm to give examples of pairing-friendly ordinary abelian varieties of dimension 2 and 3 that are absolutely simple and have smaller ρ-values than any previous such example.