VLSI Architectures for Computing Multiplications and Inverses in GF(2m)
IEEE Transactions on Computers
A Comparison of VLSI Architecture of Finite Field Multipliers Using Dual, Normal, or Standard Bases
IEEE Transactions on Computers
Journal of Cryptology
Structure of parallel multipliers for a class of fields GF(2m)
Information and Computation
A New Algorithm for Multiplication in Finite Fields
IEEE Transactions on Computers
IEEE Transactions on Computers
IEEE Transactions on Computers - Special issue on computer arithmetic
Bit-Serial Systolic Divider and Multiplier for Finite Fields GF(2/sup m/)
IEEE Transactions on Computers - Special issue on computer arithmetic
VLSI algorithms and architectures for real-time computation over finite fields
VLSI algorithms and architectures for real-time computation over finite fields
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Reed-Solomon Codes and Their Applications
Reed-Solomon Codes and Their Applications
Fast Algorithms for Digital Signal Processing
Fast Algorithms for Digital Signal Processing
Handbook of Applied Cryptography
Handbook of Applied Cryptography
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
IEEE Transactions on Computers
VLSI Designs for Multiplication over Finite Fields GF (2m)
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Efficient computations in galois fields
Efficient computations in galois fields
Efficient Normal Basis Multipliers in Composite Fields
IEEE Transactions on Computers
A New Construction of Massey-Omura Parallel Multiplier over GF(2^{m})
IEEE Transactions on Computers
Montgomery Multiplier and Squarer for a Class of Finite Fields
IEEE Transactions on Computers
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
Modular Multiplication in GF(pk) Using Lagrange Representation
INDOCRYPT '02 Proceedings of the Third International Conference on Cryptology: Progress in Cryptology
A New Approach to Subquadratic Space Complexity Parallel Multipliers for Extended Binary Fields
IEEE Transactions on Computers
An area-efficient bit-serial integer and GF(2n) multiplier
Microelectronic Engineering
Computers and Electrical Engineering
Low-complexity bit-parallel dual basis multipliers using the modified Booth's algorithm
Computers and Electrical Engineering
Efficient bit-parallel multipliers over finite fields GF(2m)
Computers and Electrical Engineering
Information Processing Letters
Modified sequential normal basis multipliers for type II optimal normal bases
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part II
A non-redundant and efficient architecture for karatsuba-ofman algorithm
ISC'05 Proceedings of the 8th international conference on Information Security
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
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This contribution introduces a new class of multipliers for finite fields GF((2n)4). The architecture is based on a modified version of the Karatsuba-Ofman algorithm (KOA). By determining optimized field polynomials of degree four, the last stage of the KOA and the modulo reduction can be combined. This saves computation and area in VLSI implementations. The new algorithm leads to architectures which show a considerably improved gate complexity compared to traditional approaches and reduced delay if compared with KOA-based architectures with separate modulo reduction. The new multipliers lead to highly modular architectures and are, thus, well suited for VLSI implementations. Three types of field polynomials are introduced and conditions for their existence are established. For the small fields, where n = 2, 3, ..., 8, which are of primary technical interest, optimized field polynomials were determined by an exhaustive search. For each field order, exact space and time complexities are provided.