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We present a lower bound on parallel exponentiation in the model of weighted <italic>q</italic>-addition chains which neglects communication. We derive an algorithm which covers results of Kung  and von zur Gathen . For an actual implementation the (fixed) number of processors and the communication delay have to be taken into account. We develop… (More)
We study exponentiation in finite fields with very special exponents such as they occur, e.g., in inversion and in primit.ivity tests. Our algorit.hmic approach improves the corrcspending exponentiation problem from about qimtlratic to about liIM!ifl time.
We study exponentiation in nonprime finite fields with very special exponents such as they occur, for example, in inversion, primitivity tests, and polynomial factorization. Our algorithmic approach improves the corresponding exponentiation problem from about quadratic to about linear time.
We discuss two different ways to speed up exponentiation in nonprime finite fields: on the one hand, reduction of the total number of operations, and on the other hand, fast computation of a single operation. Two data structures are particularly useful: sparse irreducible polynomials and normal bases. We report on implementation results for our methods.