Finite field for scientists and engineers
Finite field for scientists and engineers
IRSIM: an incremental MOS switch-level simulator
DAC '89 Proceedings of the 26th ACM/IEEE Design Automation Conference
IEEE Transactions on Computers
Reed-Solomon Codes and Their Applications
Reed-Solomon Codes and Their Applications
A Systolic Power-Sum Circuit for GF(2/sup m/)
IEEE Transactions on Computers
Bit-Level Systolic Array for Fast Exponentiation in GF(2/sup m/)
IEEE Transactions on Computers
Efficient Finite Field Serial/Parallel Multiplication
ASAP '96 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
Efficient standard basis Reed-Solomon encoder
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 06
Systolic Multipliers for Finite Fields GF(2m)
IEEE Transactions on Computers
A Cellular-Array Multiplier for GF(2m)
IEEE Transactions on Computers
Low-Energy Digit-Serial/Parallel Finite Field Multipliers
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
Total System Energy Minimization for Wireless Image Transmission
Journal of VLSI Signal Processing Systems - Special issue on multimedia signal processing
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Low Complexity Bit Serial Systolic Multipliers over GF(2m) for Three Classes of Finite Fields
ICICS '02 Proceedings of the 4th International Conference on Information and Communications Security
A Power-Sum Systolic Architecture in GF(2m)
ICOIN '02 Revised Papers from the International Conference on Information Networking, Wireless Communications Technologies and Network Applications-Part II
Parallel Algorithm and Architecture for Public-Key Cryptosystem
EurAsia-ICT '02 Proceedings of the First EurAsian Conference on Information and Communication Technology
Area Efficient Exponentiation Using Modular Multiplier/Squarer in GF(2m
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Inversion/Division Systolic Architecture for Public-Key Cryptosystems in GF(2m)
ISC '02 Proceedings of the 5th International Conference on Information Security
Hardware architectures for public key cryptography
Integration, the VLSI Journal
A digit-serial multiplier for finite field GF(2m)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Low-complexity versatile finite field multiplier in normal basis
EURASIP Journal on Applied Signal Processing
A Novel Architecture for Galois Fields GF(2^m) Multipliers Based on Mastrovito Scheme
IEEE Transactions on Computers
Versatile multiplier architectures in GF(2k) fields using the Montgomery multiplication algorithm
Integration, the VLSI Journal
Semi-systolic Modular Multiplier over GF(2m)
ICCSA '08 Proceedings of the international conference on Computational Science and Its Applications, Part II
Computers and Electrical Engineering
Extended sequential logic for synchronous circuit optimization and its applications
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Test generation in systolic architecture for multiplication over GF(2m)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
On efficient implementation of accumulation in finite field over GF(2m) and its applications
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A security scheme for dependable key insertion in mobile embedded devices
International Journal of Reconfigurable Computing - Special issue on selected papers from the international workshop on reconfigurable communication-centric systems on chips (ReCoSoC' 2010)
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and its Applications - Volume Part I
Semi-systolic architecture for modular multiplication over GF(2m)
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
Low complexity systolic architecture for modular multiplication over GF(2m)
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part I
VLSI performance evaluation and analysis of systolic and semisystolic finite field multipliers
ACSAC'05 Proceedings of the 10th Asia-Pacific conference on Advances in Computer Systems Architecture
Unidirectional two dimensional systolic array for multiplication in GF(2m) using LSB first algorithm
WILF'05 Proceedings of the 6th international conference on Fuzzy Logic and Applications
Low latency systolic montgomery multiplier for finite field GF(2m) based on pentanomials
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Hi-index | 0.00 |
Finite fields have been used for numerous applications including error-control coding and cryptography. The design of efficient multipliers, dividers, and exponentiators for finite field arithmetic is of great practical concern. In this paper, we explore and classify algorithms for finite field multiplication, squaring, and exponentiation into least significant bit first (LSBfirst) scheme and most significant bit first (MSB-first) scheme, and implement these algorithms using semisystolic arrays. For finite field multiplication (for programmable as well as fixed field order) and exponentiation, we conclude that LSB-first algorithms are more efficient as their basic cells have less critical path computation time. Another advantage of LSB-first scheme is its capability of achieving substructure sharing among multiple operations, which could lead to savings in hardware when these arithmetic units are used as building blocks for a large system. For finite field squaring operation, it turns out that the MSB-first algorithm is more efficient as it leads to simpler architectures. Bitlevel pipelined semisystolic architectures utilize broadcast signals. As a result, these require much less number of latches and lead to much smaller latency than the corresponding systolic array, with the same cycle time (the computation time in one basic cell). Efficient VLSI implementation of semisystolic multipliers, squarers and exponentiators are designed and compared with existing architectures. A novel architecture for computing ABn+ C using power representation is also presented.