Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Supersingular Abelian Varieties in Cryptology
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Constructing elliptic curves with given group order over large finite fields
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Efficient Implementation of Pairing-Based Cryptosystems
Journal of Cryptology
Short Signatures from the Weil Pairing
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)
Building Curves with Arbitrary Small MOV Degree over Finite Prime Fields
Journal of Cryptology
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
Building cyclic elliptic curves modulo large primes
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Constructing elliptic curves with prescribed embedding degrees
SCN'02 Proceedings of the 3rd international conference on Security in communication networks
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
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
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
Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2 = x5 + ax
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
Tracing Malicious Proxies in Proxy Re-encryption
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
More Discriminants with the Brezing-Weng Method
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
Compact Proofs of Retrievability
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
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
A Strongly Unforgeable Signature under the CDH Assumption without Collision Resistant Hash Functions
IEICE - Transactions on Information and Systems
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
Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
Security of Verifiably Encrypted Signatures and a Construction without Random Oracles
Pairing '09 Proceedings of the 3rd International Conference Palo Alto on Pairing-Based Cryptography
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
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
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 and generalized pairing computation on Abelian varieties
IEEE Transactions on Information Theory
Multi-core Implementation of the Tate Pairing over Supersingular Elliptic Curves
CANS '09 Proceedings of the 8th International Conference on Cryptology and Network Security
Distributing the Key Distribution Centre in Sakai---Kasahara Based Systems
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Practical Zero-Knowledge Proofs for Circuit Evaluation
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
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
Elliptic curves with a pre-determined embedding degree
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Pairing-friendly elliptic curves with small security loss by Cheon's algorithm
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
A CDH-based strongly unforgeable signature without collision resistant hash function
ProvSec'07 Proceedings of the 1st international conference on Provable security
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
On compressible pairings and their computation
AFRICACRYPT'08 Proceedings of the Cryptology in Africa 1st international conference on Progress in cryptology
IEEE Transactions on Information Theory
A pairing-based DAA scheme further reducing TPM resources
TRUST'10 Proceedings of the 3rd international conference on Trust and trustworthy computing
An anonymous attestation scheme with optional traceability
TRUST'10 Proceedings of the 3rd international conference on Trust and trustworthy computing
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
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
Efficient implementation of pairing on BREW mobile phones
IWSEC'10 Proceedings of the 5th international conference on Advances in information and computer security
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
Generating more Kawazoe-Takahashi genus 2 pairing-friendly hyperelliptic curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Compact hardware for computing the tate pairing over 128-bit-security supersingular 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
High speed flexible pairing cryptoprocessor on FPGA platform
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
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
Non-interactive distributed encryption: a new primitive for revocable privacy
Proceedings of the 10th annual ACM workshop on Privacy in the electronic society
Security of prime field pairing cryptoprocessor against differential power attack
InfoSecHiComNet'11 Proceedings of the First international conference on Security aspects in information technology
Cryptographic pairings based on elliptic nets
IWSEC'11 Proceedings of the 6th International conference on Advances in information and computer security
Efficient intrusion-resilient signatures without random oracles
Inscrypt'06 Proceedings of the Second SKLOIS conference on Information Security and Cryptology
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Concise mercurial vector commitments and independent zero-knowledge sets with short proofs
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
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
Universal designated verifier signatures without random oracles or non-black box assumptions
SCN'06 Proceedings of the 5th international conference on Security and Cryptography for Networks
Avoiding full extension field arithmetic in pairing computations
AFRICACRYPT'10 Proceedings of the Third international conference on Cryptology in Africa
On constructing certificateless cryptosystems from identity based encryption
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Sequential aggregate signatures and multisignatures without random oracles
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Developing efficient blinded attribute certificates on smart cards via pairings
CARDIS'10 Proceedings of the 9th IFIP WG 8.8/11.2 international conference on Smart Card Research and Advanced Application
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
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
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
Short signatures from weaker assumptions
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
Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
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
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
TCC'12 Proceedings of the 9th international conference on Theory of 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
Group to group commitments do not shrink
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Solving a discrete logarithm problem with auxiliary input on a 160-bit elliptic curve
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
Implementing cryptographic pairings
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
Remarks on Cheon's algorithms for pairing-related problems
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Indifferentiable hashing to barreto---naehrig curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
SMSCrypto: A lightweight cryptographic framework for secure SMS transmission
Journal of Systems and Software
Computing on authenticated data: new privacy definitions and constructions
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Sequential aggregate signatures with lazy verification from trapdoor permutations
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
Shorter IBE and signatures via asymmetric pairings
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
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
Improved broadcast encryption scheme with constant-size ciphertext
Pairing'12 Proceedings of the 5th international conference on Pairing-Based Cryptography
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
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
Using SMT solvers to automate design tasks for encryption and signature schemes
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
NEON implementation of an attribute-based encryption scheme
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
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
Towards a practical cryptographic voting scheme based on malleable proofs
Vote-ID'13 Proceedings of the 4th international conference on E-Voting and Identity
A more efficient computationally sound non-interactive zero-knowledge shuffle argument
Journal of Computer Security - Advances in Security for Communication Networks
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Previously known techniques to construct pairing-friendly curves of prime or near-prime order are restricted to embedding degree $k \leqslant 6 $. More general methods produce curves over ${\mathbb F}_{p}$ where the bit length of p is often twice as large as that of the order r of the subgroup with embedding degree k; the best published results achieve ρ ≡ log(p)/log(r) ~ 5/4. In this paper we make the first step towards surpassing these limitations by describing a method to construct elliptic curves of prime order and embedding degree k = 12. The new curves lead to very efficient implementation: non-pairing operations need no more than ${\mathbb F}_{p^4}$ arithmetic, and pairing values can be compressed to one third of their length in a way compatible with point reduction techniques. We also discuss the role of large CM discriminants D to minimize ρ; in particular, for embedding degree k = 2q where q is prime we show that the ability to handle log(D)/log(r) ~ (q–3)/(q–1) enables building curves with ρ ~ q/(q–1).