A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
International Journal of Information Security
Optimised versions of the ate and twisted ate pairings
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
IEEE Transactions on Information Theory
Computing bilinear pairings on elliptic curves with automorphisms
Designs, Codes and Cryptography
An improved twisted ate pairing over KSS curves with k=18
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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In this paper, we suggest that all pairings are in a group from an abstract angle. Based on the results, some new pairings with the short Miller loop are constructed for great efficiency. It is possible that our observation can be applied into other aspects of pairing-based cryptosystems.