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
Algebraic aspects of cryptography
Algebraic aspects of cryptography
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
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
Algebraic Function Fields and Codes
Algebraic Function Fields and Codes
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 tate pairing computation for elliptic curves over binary fields
ACISP'05 Proceedings of the 10th Australasian conference on Information Security and Privacy
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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
On Supersingular Abelian Varieties of Dimension Two over Finite Fields
Finite Fields and Their Applications
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Improved Implementations of Cryptosystems Based on Tate Pairing
ISA '09 Proceedings of the 3rd International Conference and Workshops on Advances in Information Security and Assurance
Generating Pairing-Friendly Curves with the CM Equation of Degree 1
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Accelerating twisted ate pairing with frobenius map, small scalar multiplication, and multi-pairing
ICISC'09 Proceedings of the 12th international conference on Information security and cryptology
On the efficiency and security of pairing-based protocols in the type 1 and type 4 settings
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
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
Delaying mismatched field multiplications in pairing computations
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Efficient implementation of pairing on BREW mobile phones
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
Computing bilinear pairings on elliptic curves with automorphisms
Designs, Codes and Cryptography
An analysis of affine coordinates for pairing computation
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Faster pairing computation on genus 2 hyperelliptic curves
Information Processing Letters
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
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
Cryptographic pairings based on elliptic nets
IWSEC'11 Proceedings of the 6th International conference on Advances in information and computer security
A method for efficient parallel computation of Tate pairing
International Journal of Grid and Utility Computing
Faster squaring in the cyclotomic subgroup of sixth degree extensions
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Avoiding full extension field arithmetic in pairing computations
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
High-speed parallel software implementation of the ηT pairing
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Parallelizing the weil and tate pairings
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
On the efficient implementation of pairing-based protocols
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
On efficient pairings on elliptic curves over extension fields
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
An improved twisted ate pairing over KSS curves with k=18
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Faster pairing coprocessor architecture
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
Simple and exact formula for minimum loop length in Atei pairing based on Brezing---Weng curves
Designs, Codes and Cryptography
International Journal of Applied Cryptography
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In this paper, we propose a new method for constructing a bilinear pairing over (hyper)elliptic curves, which we call the R-ate pairing. This pairing is a generalization of the Ate and Atei pairing, and can be computed more efficiently. Using the R-ate pairing, the loop length in Miller's algorithm can be as small as log(r1/Φ(k)) for some pairing-friendly elliptic curves which have not reached this lower bound. Therefore, we obtain savings of between 29% and 69% in overall costs compared to the Atei pairing. On supersingular hyperelliptic curves of genus 2, we show that this approach makes the loop length in Miller's algorithm shorter than that of the Ate pairing.