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Efficient Exponentiation of a Primitive Root in GF(2m)
February 1997 (vol. 46 no. 2)
pp. 162-172

Abstract—In this paper, exponentiation of a primitive root in GF(2m) is considered. Signed digit (SD) number representation is used to efficiently represent the exponent and the corresponding algorithms and structures for exponentiation are developed. For primitive multiplications required in exponentiations, extended bidirectional linear feedback shift registers are proposed and used for the cases where the exponent is represented as a binary or a radix-4 SD number. Comparisons are made with other methods on the bases of space, time, and possible power consumption. Since the proposed structures can effectively reduce power and area when implemented in VLSI, they are especially suitable for battery powered portable devices.

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Index Terms:
Exponentiation, Galois or finite fields, signed digit number, minimal representation, LFSR, primitive root.
Huapeng Wu, M. Anwarul Hasan, "Efficient Exponentiation of a Primitive Root in GF(2m)," IEEE Transactions on Computers, vol. 46, no. 2, pp. 162-172, Feb. 1997, doi:10.1109/12.565591
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