Primitive root-finding problem: Difference between revisions
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==Definition== | ==Definition== | ||
Suppose <math>G</math> is a [[finite group]] specified by means of a suitable [[group description rule]] (typically, an [[encoding of a group|encoding]]), and we are given a promise that <math>G</matH> is a [[finite cyclic group]]. The goal is to obtain an explicit description of a single element <math>g \in G</math> such that <math>G = \langle g \rangle</math>. Such an element is termed a ''primitive root'' in some contexts. | Suppose <math>G</math> is a [[finite group]] specified by means of a suitable [[group description rule]] (typically, an [[encoding of a group|encoding]]), and we are given a promise that <math>G</matH> is a [[finite cyclic group]]. In other words, we can think of <math>G</math> as a [[black-box cyclic group]] (though there may be more contextual structure known about <math>G</math>). The goal is to obtain an explicit description of a single element <math>g \in G</math> such that <math>G = \langle g \rangle</math>. Such an element is termed a ''primitive root'' in some contexts. | ||
Latest revision as of 21:07, 25 June 2013
Definition
Suppose is a finite group specified by means of a suitable group description rule (typically, an encoding), and we are given a promise that is a finite cyclic group. In other words, we can think of as a black-box cyclic group (though there may be more contextual structure known about ). The goal is to obtain an explicit description of a single element such that . Such an element is termed a primitive root in some contexts.