A New Finite-Field Multiplier Using Redundant Representation

A novel serial-in parallel-out finite field multiplier using redundant representation is proposed. It is shown that the proposed architecture has either a significantly lower complexity and comparable critical path delay or a significantly smaller critical path delay and comparable complexity in comparison to the previously proposed architectures using the same representation. For the class of fields where there exists a type I optimal normal basis, the proposed multiplier compares favorably to the normal basis multipliers. A digit-level version for the new multiplier is also presented in this paper.