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A New Algorithm for Multiplication in Finite Fields
July 1989 (vol. 38 no. 7)
pp. 1045-1049
A new algorithm is presented for computing the product of two elements in a finite field by means of sums and products in a fixed subfield. The algorithm is based on a normal basis representation of fields and assumes that the dimension m of the finite field over the subfield is a highly composite number. A very fast parallel implementation and a considerable reduction in the number of computat

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Index Terms:
algorithm; multiplication; finite fields; sums and products; normal basis representation; highly composite number; parallel implementation; parallel algorithms.
A. Pincin, "A New Algorithm for Multiplication in Finite Fields," IEEE Transactions on Computers, vol. 38, no. 7, pp. 1045-1049, July 1989, doi:10.1109/12.30855
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