Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
An RNS Montgomery Modular Multiplication Algorithm
IEEE Transactions on Computers
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
An Identity-Based Signature from Gap Diffie-Hellman Groups
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
Implementation of RSA Algorithm Based on RNS Montgomery Multiplication
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
A One Round Protocol for Tripartite Diffie–Hellman
Journal of Cryptology
Short Signatures from the Weil Pairing
Journal of Cryptology
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
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
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
On Software Parallel Implementation of Cryptographic Pairings
Selected Areas in Cryptography
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
A Taxonomy of Pairing-Friendly Elliptic Curves
Journal of Cryptology
Cox-Rower architecture for fast parallel montgomery multiplication
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
IEEE Transactions on Information Theory
A high speed coprocessor for elliptic curve scalar multiplications over Fp
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
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
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
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
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
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
High-speed parallel software implementation of the ηT pairing
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
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
Efficient Hardware Implementation of Fp-Arithmetic for Pairing-Friendly Curves
IEEE Transactions on Computers
IEEE Transactions on Information Theory
Implementing cryptographic pairings
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Optimal eta pairing on supersingular genus-2 binary hyperelliptic curves
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
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
Improving modular inversion in RNS using the plus-minus method
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
| Hi-index | 0.00 |
Recently, a lot of progress has been made in the implementation of pairings in both hardware and software. In this paper, we present two FPGA-based high speed pairing designs using the Residue Number System and lazy reduction. We show that by combining RNS, which is naturally suitable for parallel architectures, and lazy reduction, which performs one reduction for multiple multiplications, the speed of pairing computation in hardware can be largely increased. The results show that both designs achieve higher speed than previous designs. The fastest version computes an optimal ate pairing at 126-bit security level in 0.573 ms, which is 2 times faster than all previous hardware implementations at the same security level.