Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Efficient Implementation of Pairing-Based Cryptosystems
Journal of Cryptology
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Efficient pairing computation on supersingular Abelian varieties
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
Discrete Applied Mathematics
Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Efficient and generalized pairing computation on Abelian varieties
IEEE Transactions on Information Theory
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
IEEE Transactions on Information Theory
Constructing tower extensions of finite fields for implementation of pairing-based cryptography
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
An analysis of affine coordinates for pairing computation
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
High-speed software implementation of the optimal ate pairing over Barreto-Naehrig curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Inner-product encryption under standard assumptions
Designs, Codes and Cryptography
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
A family of implementation-friendly BN elliptic curves
Journal of Systems and Software
Faster explicit formulas for computing pairings over ordinary curves
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Attractive subfamilies of BLS curves for implementing high-security pairings
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
On efficient pairings on elliptic curves over extension fields
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Implementing pairings at the 192-bit security level
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Speeding up ate pairing computation in affine coordinates
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Fast transmission to remote cooperative groups: a new key management paradigm
IEEE/ACM Transactions on Networking (TON)
NEON implementation of an attribute-based encryption scheme
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
Group-signature schemes on constrained devices: the gap between theory and practice
Proceedings of the First Workshop on Cryptography and Security in Computing Systems
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The advent of Pairing-based protocols has had a major impact on the applicability of cryptography to the solution of more complex real-world problems. However there has always been a question mark over the performance of such protocols. In response much work has been done to optimize pairing implementation, and now it is generally accepted that being pairing-based does not preclude a protocol from consideration as a practical proposition. However although a lot of effort has gone into the optimization of the stand-alone pairing, in many protocols the pairing calculation appears in a particular context within which further optimizations may be possible. It is the purpose of this paper to bridge the gap between theory and practice, and to show that even complex protocols may have a surprisingly efficient implementation. We also point out that in some cases the usually recommended pairing friendly curves may not in fact be optimal. We claim a new record with our implementation of a pairing at the AES-256 bit level.