Fast Multiplication in Finite Fields GF(2N)

A method is described for performing computations in a finite field GF(2N) by embedding it in a larger ring Rp where the multiplication operation is a convolution product and the squaring operation is a rearrangement of bits. Multiplication in Rp has complexity N +1, which is approximately twice as efficient as optimal normal basis multiplication (ONB) or Montgomery multiplication in GF(2N), while squaring has approximately the same efficiency as ONB. Inversion and solution of quadratic equations can also be performed at least as fast as previous methods.

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