A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Low-Energy Digit-Serial/Parallel Finite Field Multipliers
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
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
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
A One Round Protocol for Tripartite Diffie-Hellman
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
The Weil Pairing, and Its Efficient Calculation
Journal of Cryptology
Parallel Hardware Architectures for the Cryptographic Tate Pairing
ITNG '06 Proceedings of the Third International Conference on Information Technology: New Generations
Hardware acceleration of the Tate pairing on a genus 2 hyperelliptic curve
Journal of Systems Architecture: the EUROMICRO Journal
Efficient pairing computation on supersingular Abelian varieties
Designs, Codes and Cryptography
Hardware architectures for the Tate pairing over GF(2m)
Computers and Electrical Engineering
Elliptic Curves: Number Theory and Cryptography, Second Edition
Elliptic Curves: Number Theory and Cryptography, Second Edition
An Efficient Hardware Implementation of the Tate Pairing in Characteristic Three
ICONS '08 Proceedings of the Third International Conference on Systems
A FPGA Coprocessor for the Cryptographic Tate Pairing over Fp
ITNG '08 Proceedings of the Fifth International Conference on Information Technology: New Generations
A Coprocessor for the Final Exponentiation of the ηTPairing in Characteristic Three
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
Algorithms and Arithmetic Operators for Computing the ηT Pairing in Characteristic Three
IEEE Transactions on Computers
FPGA implementations of elliptic curve cryptography and Tate pairing over a binary field
Journal of Systems Architecture: the EUROMICRO Journal
FPGA and ASIC implementations of the ηT pairing in characteristic three
Computers and Electrical Engineering
A long note on Mulders' short product
Journal of Symbolic Computation
Explicit formulas for efficient multiplication in F36m
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
A flexible processor for the characteristic 3 ηT pairing
International Journal of High Performance Systems Architecture
High security pairing-based cryptography revisited
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Collusion resistant broadcast encryption with short ciphertexts and private keys
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Hardware acceleration of the tate pairing in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
Efficient hardware for the tate pairing calculation in characteristic three
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
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
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
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
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This paper is devoted to the design of fast parallel accelerators for the cryptographic Tate pairing in characteristic three over supersingular elliptic curves. We propose here a novel hardware implementation of Miller's loop based on a pipelined Karatsuba-Ofman multiplier. Thanks to a careful selection of algorithms for computing the tower field arithmetic associated to the Tate pairing, we manage to keep the pipeline busy. We also describe the strategies we considered to design our parallel multiplier. They are included in a VHDL code generator allowing for the exploration of a wide range of operators. Then, we outline the architecture of a coprocessor for the Tate pairing over $\mathbb{F}_{3^m}$. However, a final exponentiation is still needed to obtain a unique value, which is desirable in most of the cryptographic protocols. We supplement our pairing accelerator with a coprocessor responsible for this task. An improved exponentiation algorithm allows us to save hardware resources. According to our place-and-route results on Xilinx FPGAs, our design improves both the computation time and the area-time trade-off compared to previoulsy published coprocessors.