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Monte Carlo Methods for Index Computation $(\operatorname{mod} p)$

J. M. Pollard
Mathematics of Computation
Vol. 32, No. 143 (Jul., 1978), pp. 918-924
DOI: 10.2307/2006496
Stable URL: http://www.jstor.org/stable/2006496
Page Count: 7
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Monte Carlo Methods for Index Computation $(\operatorname{mod} p)$
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Abstract

We describe some novel methods to compute the index of any integer relative to a given primitive root of a prime $p$. Our first method avoids the use of stored tables and apparently requires $O(p^{1/2})$ operations. Our second algorithm, which may be regarded as a method of catching kangaroos, is applicable when the index is known to lie in a certain interval; it requires $O(w^{1/2})$ operations for an interval of width $w$, but does not have complete certainty of success. It has several possible areas of application, including the factorization of integers.

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