Introduction to finite fields and their applications
Introduction to finite fields and their applications
Structure of parallel multipliers for a class of fields GF(2m)
Information and Computation
IEEE Transactions on Computers - Special issue on computer arithmetic
Low-Complexity Bit-Parallel Canonical and Normal Basis Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Low Complexity Bit-Parallel Multipliers for a Class of Finite Fields
IEEE Transactions on Computers
Double-Basis Multiplicative Inversion Over GF(2m)
IEEE Transactions on Computers
Mastrovito Multiplier for All Trinomials
IEEE Transactions on Computers
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
Architecture For A Low Complexity Rate-Adaptive Reed-Solomon Encoder
IEEE Transactions on Computers
GF(2m) Multiplication and Division Over the Dual Basis
IEEE Transactions on Computers
Bit-Parallel Finite Field Multiplier and Squarer Using Polynomial Basis
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
An efficient technique for synthesis and optimization of polynomials in GF(2m)
Proceedings of the 2006 IEEE/ACM international conference on Computer-aided design
Low complexity bit parallel multiplier for GF (2m) generated by equally-spaced trinomials
Information Processing Letters
Digit-Serial Structures for the Shifted Polynomial Basis Multiplication over Binary Extension Fields
WAIFI '08 Proceedings of the 2nd international workshop on Arithmetic of Finite Fields
Low complexity bit-parallel multipliers based on a class of irreducible pentanomials
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
Integration, the VLSI Journal
New bit parallel multiplier with low space complexity for all irreducible trinomials over GF(2n)
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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A new formulation for the canonical basis multiplication in the finite fields GF(2^m) based on the use of a triangular basis and on the decomposition of a product matrix is presented. From this algorithm, a new method for multiplication (named transpositional) applicable to general irreducible polynomials is deduced. The transpositional method is based on the computation of 1-cycles and 2--cycles given by a permutation defined by the coordinate of the product to be computed and by the cardinality of the field GF(2^m). The obtained cycles define groups corresponding to subexpressions that can be shared among the different product coordinates. This new multiplication method is applied to five types of irreducible trinomials. These polynomials have been widely studied due to their low-complexity implementations. The theoretical complexity analysis of the corresponding bit-parallel multipliers shows that the space complexities of our multipliers match the best results known to date for similar canonical GF(2^m) multipliers. The most important new result is the reduction, in two of the five studied trinomials, of the time complexity with respect to the best known results.