New Systolic Arrays for C + AB2, Inversion, and Division in GF(2m)

  • Authors:
  • Chin-Liang Wang;Jyh-Huei Guo

  • Affiliations:
  • National Tsing Hua Univ., Hsinchu, Taiwan;Winbond Electronics Corp., Hsinchu, Taiwan

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 2000

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Abstract

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(2m). 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(2m). The proposed systolic divider gains advantages over an existing system with the same throughput performance in terms of chip area, latency, and fault tolerance.