Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Hierarchical ID-Based Cryptography
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Hessian Elliptic Curves and Side-Channel Attacks
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
The Hessian Form of an Elliptic Curve
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
A One Round Protocol for Tripartite Diffie–Hellman
Journal of Cryptology
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Pairing Computation on Twisted Edwards Form Elliptic Curves
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Another Approach to Pairing Computation in Edwards Coordinates
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Faster Pairings on Special Weierstrass Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
Aggregate and verifiably encrypted signatures from bilinear maps
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Optimised versions of the ate and twisted ate pairings
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Efficient pairing computation on Elliptic curves in Hessian form
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Efficient computation of tate pairing in projective coordinate over general characteristic fields
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
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
Efficient arithmetic on hessian curves
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
The tate pairing via elliptic nets
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Fast tate pairing computation on twisted Jacobi intersections curves
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
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This paper considers a model for elliptic curve named Selmer curves. We study the arithmetic of Selmer curves, which includes group operations and pairing computation. We present fast formulae for point addition and doubling. Moreover, for even embedding degree k, we show that Tate pairing computation on Selmer curves is very efficient. It is almost the fastest among that on various elliptic curve models such as Weierstrass curves, Edwards curves, Hessian curves, etc.. One more advantage which Selmer curves gain over other models is that pairing computation on this model can be performed in a parallel manner. In addition, the higher twists (up to sextic twists) technique can also be applied to Selmer curves for accelerating pairing computation. We finally present some numerical examples of pairing friendly Selmer curves which can employ sextic twists.