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| M.A. Hasan, M. Wang, V.K. Bhargava, "Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields GF(2/sup m/)," IEEE Transactions on Computers, vol. 41, no. 8, pp. 962-971, August, 1992. | |||
| BibTex | x | ||
| @article{ 10.1109/12.156539, author = {M.A. Hasan and M. Wang and V.K. Bhargava}, title = {Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields GF(2/sup m/)}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {8}, issn = {0018-9340}, year = {1992}, pages = {962-971}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.156539}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Modular Construction of Low Complexity Parallel Multipliers for a Class of Finite Fields GF(2/sup m/) IS - 8 SN - 0018-9340 SP962 EP971 EPD - 962-971 A1 - M.A. Hasan, A1 - M. Wang, A1 - V.K. Bhargava, PY - 1992 KW - squaring algorithms; parallel multipliers; finite fields; irreducible all one polynomials; equally spaced polynomials; multiplication algorithms; exponentiation; inversion; complexity; computational complexity; digital arithmetic; multiplying circuits; number theory. VL - 41 JA - IEEE Transactions on Computers ER - | |||
Structures for parallel multipliers of a class of fields GF(2/sup m/) based on irreducible all one polynomials (AOP) and equally spaced polynomials (ESP) are presented. The structures are simple and modular, which is important for hardware realization. Relationships between an irreducible AOP and the corresponding irreducible ESPs have been exploited to construct ESP-based multipliers of large fields by a regular expansion of the basic modules of the AOP-based multiplier of a small field. Some features of the structures also enable a fast implementation of squaring and multiplication algorithms and therefore make fast exponentiation and inversion possible. It is shown that, if for a certain degree, an irreducible AOP as well as an irreducible ESP exist, then from the complexity point of view, it is advantageous to use the ESP-based parallel multiplier.
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