A course in number theory and cryptography
A course in number theory and cryptography
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
A course in computational algebraic number theory
A course in computational algebraic number theory
Finite fields
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Function field sieve method for discrete logarithms over finite fields
Information and Computation
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
The Special Function Field Sieve
SIAM Journal on Discrete Mathematics
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
An Elliptic Curve Implementation of the Finite Field Digital Signature Algorithm
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Unbelievable Security. Matching AES Security Using Public Key Systems
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: 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
FC '00 Proceedings of the 4th International Conference on Financial Cryptography
Discrete Logarithms: The Effectiveness of the Index Calculus Method
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Postal Revenue Collection in the Digital Age
FC '00 Proceedings of the 4th International Conference on Financial Cryptography
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
A One Round Protocol for Tripartite Diffie–Hellman
Journal of Cryptology
Evidence that XTR Is More Secure than Supersingular Elliptic Curve Cryptosystems
Journal of Cryptology
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Elliptic Curves Suitable for Pairing Based Cryptography
Designs, Codes and Cryptography
Generating More MNT Elliptic Curves
Designs, Codes and Cryptography
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
On the discrete logarithm problem on algebraic tori
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Collusion resistant broadcast encryption with short ciphertexts and private keys
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Efficient identity-based encryption without random oracles
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Hierarchical identity based encryption with constant size ciphertext
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
On the relationship between squared pairings and plain pairings
Information Processing Letters
An efficient identity-based signature scheme with batch verifications
InfoScale '06 Proceedings of the 1st international conference on Scalable information systems
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
Arithmetic Operators for Pairing-Based Cryptography
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Pairing Computation on Twisted Edwards Form Elliptic Curves
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
Another Approach to Pairing Computation in Edwards Coordinates
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
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
A Strongly Unforgeable Signature under the CDH Assumption without Collision Resistant Hash Functions
IEICE - Transactions on Information and Systems
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
The Diffie---Hellman problem and generalization of Verheul's theorem
Designs, Codes and Cryptography
ISA '09 Proceedings of the 3rd International Conference and Workshops on Advances in Information Security and Assurance
Finite Field Multiplication Combining AMNS and DFT Approach for Pairing Cryptography
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
Faster Pairings on Special Weierstrass 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
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
On the relationship between squared pairings and plain pairings
Information Processing Letters
PET'07 Proceedings of the 7th international conference on Privacy enhancing technologies
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
A pairing-based DAA scheme further reducing TPM resources
TRUST'10 Proceedings of the 3rd international conference on Trust and trustworthy computing
Pairing-Based Onion Routing with Improved Forward Secrecy
ACM Transactions on Information and System Security (TISSEC)
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
Computing bilinear pairings on elliptic curves with automorphisms
Designs, Codes and 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
On the elliptic curves y2=x3-c with embedding degree one
Journal of Computational and Applied Mathematics
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
Efficient pairing computation on Elliptic curves in Hessian form
ICISC'10 Proceedings of the 13th international conference on Information security and 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
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
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
Security analysis of the strong diffie-hellman problem
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
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
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
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
Pairing'07 Proceedings of the First international conference on Pairing-Based 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
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
The tate pairing via elliptic nets
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
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
Implementing pairings at the 192-bit security level
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
Fast transmission to remote cooperative groups: a new key management paradigm
IEEE/ACM Transactions on Networking (TON)
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
| Hi-index | 0.06 |
In recent years cryptographic protocols based on the Weil and Tate pairings on elliptic curves have attracted much attention. A notable success in this area was the elegant solution by Boneh and Franklin [8] of the problem of efficient identity-based encryption. At the same time, the security standards for public key cryptosystems are expected to increase, so that in the future they will be capable of providing security equivalent to 128-, 192-, or 256-bit AES keys. In this paper we examine the implications of heightened security needs for pairing-based cryptosystems. We first describe three different reasons why high-security users might have concerns about the long-term viability of these systems. However, in our view none of the risks inherent in pairing-based systems are sufficiently serious to warrant pulling them from the shelves. We next discuss two families of elliptic curves E for use in pairing-based cryptosystems. The first has the property that the pairing takes values in the prime field $\mathbb{F}_p$ over which the curve is defined; the second family consists of supersingular curves with embedding degree k = 2. Finally, we examine the efficiency of the Weil pairing as opposed to the Tate pairing and compare a range of choices of embedding degree k, including k = 1 and k = 24.