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<p><b>Abstract</b>—We extend the binary algorithm invented by Stein and propose novel iterative division algorithms over <tmath>{\rm GF}(2^m)</tmath> for systolic VLSI realization. While Algorithm <it>EBg</it> is a basic prototype with guaranteed convergence in at most <tmath>2m-1</tmath> iterations, its variants, Algorithms <it>EBd</it> and <it>EBdf</it>, are designed for reduced complexity and fixed critical path delay, respectively. We show that Algorithms <it>EBd</it> and <it>EBdf</it> can be mapped to parallel-in parallel-out systolic circuits with low area-time complexities of <tmath>{\rm O}(m^2\log\log m)</tmath> and <tmath>{\rm O}(m^2)</tmath>, respectively. Compared to the systolic designs based on the extended Euclid's algorithm, our circuits exhibit significant speed and area advantages.</p>
Finite field, division, Stein's algorithm, Euclid's algorithm, systolic array.
Chien-Ming Wu, Ming-Der Shieh, Chien-Hsing Wu, Yin-Tsung Hwang, "High-Speed, Low-Complexity Systolic Designs of Novel Iterative Division Algorithms in GF(2^m)", IEEE Transactions on Computers, vol. 53, no. , pp. 375-380, March 2004, doi:10.1109/TC.2004.1261843
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