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We study exponentiation in finite fields with very special exponents such as they occur, e.g., in inversion and in prim-it.ivity tests. Our algorit.hmic approach improves the corrc-spending 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 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 [9] and von zur Gathen [13]. For an actual implementation the (fixed) number of processors and the communication delay have to be taken into account. We develop… (More)

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