Publication 2003 Issue No. 11 - November Abstract - New Systolic Architectures for Inversion and Division in GF(2^m)
New Systolic Architectures for Inversion and Division in GF(2^m)
November 2003 (vol. 52 no. 11)
pp. 1514-1519
 ASCII Text x Zhiyuan Yan, Dilip V. Sarwate, "New Systolic Architectures for Inversion and Division in GF(2^m)," IEEE Transactions on Computers, vol. 52, no. 11, pp. 1514-1519, November, 2003.
 BibTex x @article{ 10.1109/TC.2003.1244950,author = {Zhiyuan Yan and Dilip V. Sarwate},title = {New Systolic Architectures for Inversion and Division in GF(2^m)},journal ={IEEE Transactions on Computers},volume = {52},number = {11},issn = {0018-9340},year = {2003},pages = {1514-1519},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2003.1244950},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - New Systolic Architectures for Inversion and Division in GF(2^m)IS - 11SN - 0018-9340SP1514EP1519EPD - 1514-1519A1 - Zhiyuan Yan, A1 - Dilip V. Sarwate, PY - 2003KW - Finite fieldsKW - field arithmeticKW - inversionKW - divisionKW - systolicKW - extended Euclidean algorithm.VL - 52JA - IEEE Transactions on ComputersER -

Abstract—We present two systolic architectures for inversion and division in GF(2^m)based on a modified extended Euclidean algorithm. Our architectures are similar to those proposed by others in that they consist of two-dimensional arrays of computing cells and control cells with only local intercell connections and have O(m^2) area-time product. However, in comparison to similar architectures, both our architectures have critical path delays that are smaller, gate counts that range from being considerably smaller to only slightly larger, and latencies that are identical for inversion but somewhat larger for division. One architecture uses an adder or an (m + 1)-bit ring counter inside each control cell, while the other architecture distributes the ring counters into the computing cells, thereby reducing each control cell to just two gates.

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Index Terms:
Finite fields, field arithmetic, inversion, division, systolic, extended Euclidean algorithm.
Citation:
Zhiyuan Yan, Dilip V. Sarwate, "New Systolic Architectures for Inversion and Division in GF(2^m)," IEEE Transactions on Computers, vol. 52, no. 11, pp. 1514-1519, Nov. 2003, doi:10.1109/TC.2003.1244950