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
Double-Basis Multiplicative Inversion Over GF(2m)
IEEE Transactions on Computers
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
GF(2m) Multiplication and Division Over the Dual 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
Low complexity bit parallel architectures for polynomial basis multiplication over GF(2m)
IEEE Transactions on Computers
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Galois fields GF(2m) are used in modern communication systems such as computer networks, satellite links, or compact disks, and they play an important role in a wide number of technical applications. They use arithmetic operations in the Galois field, where the multiplication is the most important and one of the most complex operations. Efficient multiplier architectures are therefore specially important. In this paper, a new method for multiplication in the canonical and normal basis over GF(2m) generated by an AOP (all-one-polynomial), which we have named the transpositional method, is presented. This new approach is based on the grouping and sharing of subexpressions. The theoretical space and time complexities of the bit-parallel canonical and normal basis multipliers constructed using our approach are equal to the smallest ones found in the literature for similar methods, but the practical implementation over reconfigurable hardware using our method reduces the area requirements of the multipliers.