New systolic arrays for C+AB2, inversion, and division in GF(2m)

In this paper, we present a new parallel-in parallel-out systolic array with unidirectional data flow for performing the power-sum operation C+AB² in finite fields GF(2^m). The architecture employs the standard basis representation and can provide the maximum throughput in the sense of producing new results at a rate of one per clock cycle. It is highly regular, modular, and, thus, well-suited to VLSI implementation. As compared to a previous systolic power-sum circuit with bidirectional data flow and the same throughput performance, the proposed one has smaller latency, consumes less chip area, and can more easily incorporate fault-tolerant design. Based on the new power-sum circuit, we also propose a parallel-in parallel-out systolic array with the maximum throughput for computing inverses/divisions in GF(2^m). The proposed systolic divider gains advantages over an existing system with the same throughput performance in terms of chip area, latency, and fault tolerance