The Discrete Logarithm Problem
1993
Let G be a finite cyclic group, and let a be a generator for G. Then
$$G = \{ {\alpha ^i}|0 \leqslant i\# G\} $$
, where #G is the order of G. The discrete logarithm (logarithm) of an element β to the base α in G is an integer x such that α x = β. If x is restricted to the interval 0 ≤ x < #G then the discrete logarithm of β to the base α is unique. We typically write x = log α β.
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