On the Security of Pairing-Friendly Abelian Varieties over Non-prime Fields
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
IEEE Transactions on Information Theory
Synchronized aggregate signatures: new definitions, constructions and applications
Proceedings of the 17th ACM conference on Computer and communications security
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
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
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 new method for constructing pairing-friendly abelian surfaces
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Generating more Kawazoe-Takahashi genus 2 pairing-friendly hyperelliptic curves
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
Faster and lower memory scalar multiplication on supersingular curves in characteristic three
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
A family of implementation-friendly BN elliptic curves
Journal of Systems and Software
On the elliptic curves y2=x3-c with embedding degree one
Journal of Computational and Applied Mathematics
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
Efficient multiplication in finite field extensions of degree 5
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
A generalization of Verheul's theorem for some ordinary curves
Inscrypt'10 Proceedings of the 6th international conference on Information security and cryptology
Improved access control mechanism in vehicular ad hoc networks
ADHOC-NOW'11 Proceedings of the 10th international conference on Ad-hoc, mobile, and wireless networks
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
A method for efficient parallel computation of Tate pairing
International Journal of Grid and Utility Computing
Constant size ciphertexts in threshold attribute-based encryption
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
Converting pairing-based cryptosystems from composite-order groups to prime-order groups
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Avoiding full extension field arithmetic in pairing computations
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
On the joint security of encryption and signature, revisited
ASIACRYPT'11 Proceedings of the 17th international conference on The Theory and Application of Cryptology and Information Security
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
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
On constructing families of pairing-friendly elliptic curves with variable discriminant
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Attractive subfamilies of BLS curves for implementing high-security pairings
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Deterministic identity based signature scheme and its application for aggregate signatures
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Additively homomorphic encryption with a double decryption mechanism, revisited
ISC'12 Proceedings of the 15th international conference on Information Security
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
Shorter IBE and signatures via asymmetric pairings
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
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
Simple and exact formula for minimum loop length in Atei pairing based on Brezing---Weng curves
Designs, Codes and Cryptography
Generating pairing-friendly parameters for the CM construction of genus 2 curves over prime fields
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
Comparing the pairing efficiency over composite-order and prime-order elliptic curves
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
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Elliptic curves with small embedding degree and large prime-order subgroup are key ingredients for implementing pairing-based cryptographic systems. Such “pairing-friendly” curves are rare and thus require specific constructions. In this paper we give a single coherent framework that encompasses all of the constructions of pairing-friendly elliptic curves currently existing in the literature. We also include new constructions of pairing-friendly curves that improve on the previously known constructions for certain embedding degrees. Finally, for all embedding degrees up to 50, we provide recommendations as to which pairing-friendly curves to choose to best satisfy a variety of performance and security requirements.