Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Efficient Implementation of Pairing-Based Cryptosystems
Journal of Cryptology
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based 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
Constructing Pairing-Friendly Elliptic Curves Using Factorization of Cyclotomic Polynomials
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
A Generalized Brezing-Weng Algorithm for Constructing Pairing-Friendly Ordinary Abelian Varieties
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing Computation on Twisted Edwards Form Elliptic Curves
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
International Journal of Information Security
Another Approach to Pairing Computation in Edwards Coordinates
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Computing pairings using x-coordinates only
Designs, Codes and Cryptography
Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
On the Final Exponentiation for Calculating Pairings on Ordinary Elliptic Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Faster Pairings on Special Weierstrass Curves
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Fast Hashing to G2 on Pairing-Friendly 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
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Proceedings of the 11th IMA international conference on Cryptography and coding
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Optimised versions of the ate and twisted ate pairings
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
Constructing pairing-friendly elliptic curves using Gröbner basis reduction
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
IEEE Transactions on Information Theory
Faster pairings using an elliptic curve with an efficient endomorphism
INDOCRYPT'05 Proceedings of the 6th international conference on Cryptology in India
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
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
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
Ordinary abelian varieties having small embedding degree
Finite Fields and Their Applications
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Delaying mismatched field multiplications in pairing computations
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
A variant of Miller's formula and algorithm
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Pairing'10 Proceedings of the 4th international conference on Pairing-based 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
Another elliptic curve model for faster pairing computation
ISPEC'11 Proceedings of the 7th international conference on Information security practice and experience
FPGA implementation of pairings using residue number system and lazy reduction
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Avoiding full extension field arithmetic in pairing computations
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
Parallelizing the weil and tate pairings
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
Attractive subfamilies of BLS curves for implementing high-security pairings
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Fast tate pairing computation on twisted Jacobi intersections curves
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
On efficient pairings on elliptic curves over extension fields
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Core based architecture to speed up optimal ate pairing on FPGA platform
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Tate pairing computation on jacobi's elliptic curves
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
Hi-index | 0.00 |
Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the high-degree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.