Arithmetic Unit for Finite Field ${\rm GF}(2^{m})$

An arithmetic unit (AU) that performs all basic arithmetic operations in the finite field GF(2^m) is presented, where m is an arbitrary integer. The presented finite field AU consists of an arithmetic processor, an arithmetic logic unit, and a control unit. The proposed AU has low circuit complexity and is programmable, so that any error-correcting decoder that operates in GF(2^m) can be easily implemented with this AU.