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In this paper, an efficient digit-serial systolic array is proposed for multiplication in finite field GF() using the polynomial basis representation. The proposed systolic array is based on the most significant digit first (MSD-first) multiplication algorithm and produces multiplication results at a rate of one every "m/D" clock cycles, where D is the selected digit size. Since the inner structure of the proposed multiplier is tree-type, critical path increases logarithmically proportional to D. Therefore, the computation delay of the proposed architecture is significantly less than previously proposed digit-serial systolic multipliers whose critical path increases proportional to D. Furthermore, since the new architecture has the features of a high regularity, modularity, and unidirectional data flow, it is well suited to VLSI implementation.

A Digit Serial Multiplier Over GF(2m)Based on the MSD-first Algorithm

A Digit Serial Multiplier Over GF(2^m)Based on the MSD-first Algorithm