Finite field division based on recursive division algorithm and composite fields

A new division scheme for GF(2^m) is presented. This scheme is based on the recursive division algorithm and composite fields of the form GF(2²ⁿ) (m=2n). The new division scheme offers reduced time complexity of approximately O(2ⁿ) when compared to traditional bit-serial architectures with O(2²ⁿ). The scheme also offers lower hardware requirements when compared to bit-parallel architectures. The circuit architecture presented supports implementation in VLSI systems due to its regular and hardware efficient structures and is therefore suited to the implementation of Reed-Solomon codecs