Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Efficient Implementation of Pairing-Based Cryptosystems
Journal of Cryptology
A One Round Protocol for Tripartite Diffie–Hellman
Journal of Cryptology
The Weil Pairing, and Its Efficient Calculation
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)
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
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
Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
Faster Pairings on Special Weierstrass Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Refinements of Miller's algorithm for computing the Weil/Tate pairing
Journal of Algorithms
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
IEEE Transactions on Information Theory
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
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
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
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
A method for efficient parallel computation of Tate pairing
International Journal of Grid and Utility Computing
Efficient pairing computation on ordinary elliptic curves of embedding degree 1 and 2
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Speeding up ate pairing computation in affine coordinates
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
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Miller's algorithm is at the heart of all pairing-based cryptosystems since it is used in the computation of pairing such as that of Weil or Tate and their variants. Most of the optimizations of this algorithm involve elliptic curves of particular forms, or curves with even embedding degree, or having an equation of a special form. Other improvements involve a reduction of the number of iterations. In this article, we propose a variant of Miller's formula which gives rise to a generically faster algorithm for any pairing friendly curve. Concretely, it provides an improvement in cases little studied until now, in particular when denominator elimination is not available. It allows for instance the use of elliptic curve with embedding degree not of the form 2i3j, and is suitable for the computation of optimal pairings. We also present a version with denominator elimination for even embedding degree. In our implementations, our variant saves between 10% and 40% in running time in comparison with the usual version of Miller's algorithm without any optimization.