Efficient hardware implementations of arithmetic operations in the Galois field   $GF(2^{m})$   are highly desirable for several applications, such as coding theory, computer algebra and cryptography. Among these operations, multiplication is of special interest because it is considered the most important building block. Therefore, high-speed algorithms and hardware architectures for computing multiplication are highly required. In this paper, bit-parallel polynomial basis multipliers over the binary field    $GF(2^{m})$   generated using type II irreducible pentanomials are considered. The multiplier here presented has the lowest time complexity known to date for similar multipliers based on this type of irreducible pentanomials.
['José Luis Imaña']
High-Speed Polynomial Basis Multipliers Over $GF(2^{m})$ for Special Pentanomials