Efficient bit-serial multiplication and the discrete-time Wiener-Hopf equation over finite fields

Discrete-time Wiener-Hopf equations (DTWHEs) over finite fields are considered. It is shown that solving the DTWHE is equivalent to performing division over finite fields. The proof provides a new interpretation of the relationship between bit-serial multiplication and DTWHEs. The interpretation enables bit-serial multiplication over GF(2 ^m) to be understood more easily. As an example, bit-serial multiplication methods for multiplying any two elements that can be done without performing any transformation, or with only a simple transformation of the bases, are presented