Eta pairing computation on general divisors over hyperelliptic curves y2=xp-x+d
Journal of Symbolic Computation
A pairing SW implementation for Smart-Cards
Journal of Systems and Software
Ate Pairing on Hyperelliptic Curves
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Software Implementation of Arithmetic in
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based 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
Integer Variable Χ---Based Ate Pairing
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
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairings on Hyperelliptic Curves with a Real Model
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Discrete Applied Mathematics
Another Approach to Pairing Computation in Edwards Coordinates
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Skew Frobenius Map and Efficient Scalar Multiplication for Pairing---Based Cryptography
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
Computing pairings using x-coordinates only
Designs, Codes and Cryptography
Powered Tate Pairing Computation
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Computing the Ate Pairing on Elliptic Curves with Embedding Degree k = 9
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Revocable Group Signature Schemes with Constant Costs for Signing and Verifying
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
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
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
Forward-Secure Group Signatures from Pairings
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Faster $\mathbb{F}_p$-Arithmetic for Cryptographic Pairings on Barreto-Naehrig Curves
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Designing an ASIP for Cryptographic Pairings over Barreto-Naehrig Curves
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Efficient message authentication protocol for WSN
WSEAS Transactions on Computers
Efficient and generalized pairing computation on Abelian varieties
IEEE Transactions on Information Theory
FPGA and ASIC implementations of the ηT pairing in characteristic three
Computers and Electrical Engineering
Multi-core Implementation of the Tate Pairing over Supersingular Elliptic Curves
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Practical Zero-Knowledge Proofs for Circuit Evaluation
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Cross twisted Xate pairing with Barreto-Naehrig curve for multi-pairing technique
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Optimised versions of the ate and twisted ate pairings
Cryptography and Coding'07 Proceedings of the 11th IMA international conference on Cryptography and coding
NanoECC: testing the limits of elliptic curve cryptography in sensor networks
EWSN'08 Proceedings of the 5th European conference on Wireless sensor networks
An efficient countermeasure against side channel attacks for pairing computation
ISPEC'08 Proceedings of the 4th international conference on Information security practice and experience
On compressible pairings and their computation
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
On prime-order elliptic curves with embedding degrees k = 3, 4, and 6
ANTS-VIII'08 Proceedings of the 8th international conference on Algorithmic number theory
IEEE Transactions on Information Theory
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
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
New software speed records for cryptographic pairings
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
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
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
Designing a code generator for pairing based cryptographic functions
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
High speed flexible pairing cryptoprocessor on FPGA platform
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
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
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
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
On the design and implementation of an efficient DAA scheme
CARDIS'10 Proceedings of the 9th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Application
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
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
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
Attractive subfamilies of BLS curves for implementing high-security pairings
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Implementing the 4-dimensional GLV method on GLS elliptic curves with j-invariant 0
Designs, Codes and Cryptography
Progression-free sets and sublinear pairing-based non-interactive zero-knowledge arguments
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Closed formulae for the Weil pairing inversion
Finite Fields and Their Applications
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Implementing cryptographic pairings over barreto-naehrig curves
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Instruction set extensions for pairing-based cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Eta pairing computation on general divisors over hyperelliptic curves y2 = x7 - x ± 1
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
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
Implementing pairings at the 192-bit security level
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
Speeding up ate pairing computation in affine coordinates
ICISC'12 Proceedings of the 15th international conference on Information Security and Cryptology
Secure dual-core cryptoprocessor for pairings over Barreto-Naehrig curves on FPGA platform
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Improved side channel attacks on pairing based cryptography
COSADE'13 Proceedings of the 4th international conference on Constructive Side-Channel Analysis and Secure Design
Inverting the final exponentiation of tate pairings on ordinary elliptic curves using faults
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
A more efficient computationally sound non-interactive zero-knowledge shuffle argument
Journal of Computer Security - Advances in Security for Communication Networks
| Hi-index | 754.96 |
In this paper, we simplify and extend the Eta pairing, originally discovered in the setting of supersingular curves by Barreto , to ordinary curves. Furthermore, we show that by swapping the arguments of the Eta pairing, one obtains a very efficient algorithm resulting in a speed-up of a factor of around six over the usual Tate pairing, in the case of curves that have large security parameters, complex multiplication by an order of Qopf (radic-3), and when the trace of Frobenius is chosen to be suitably small. Other, more minor savings are obtained for more general curves