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High-Speed, Low-Complexity Systolic Designs of Novel Iterative Division Algorithms in GF(2^m)
March 2004 (vol. 53 no. 3)
pp. 375-380

Abstract—We extend the binary algorithm invented by Stein and propose novel iterative division algorithms over {\rm GF}(2^m) for systolic VLSI realization. While Algorithm EBg is a basic prototype with guaranteed convergence in at most 2m-1 iterations, its variants, Algorithms EBd and EBdf, are designed for reduced complexity and fixed critical path delay, respectively. We show that Algorithms EBd and EBdf can be mapped to parallel-in parallel-out systolic circuits with low area-time complexities of {\rm O}(m^2\log\log m) and {\rm O}(m^2), respectively. Compared to the systolic designs based on the extended Euclid's algorithm, our circuits exhibit significant speed and area advantages.

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Index Terms:
Finite field, division, Stein's algorithm, Euclid's algorithm, systolic array.
Citation:
Chien-Hsing Wu, Chien-Ming Wu, Ming-Der Shieh, 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. 3, pp. 375-380, March 2004, doi:10.1109/TC.2004.1261843
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