GF(2n) bit-parallel squarer using generalised polynomial basis for new class of irreducible pentanomials

Explicit formulae and complexities of bit-parallel GF(2ⁿ) squarers for a new class of irreducible pentanomials xⁿ + x^n-1 + x^k + x + 1, where n is odd and 1 <; k <; (n - 1)/2 are presented. The squarer is based on the generalised polynomial basis of GF(2ⁿ). Its gate delay matches the best results, whereas its XOR gate complexity is n + 1, which is only about two thirds of the current best results.