Multiplicative group of a prime field

Definition
Let $$p$$ be a prime. The multiplicative group of the prime field for the prime $$p$$, is defined in the following equivalent ways:


 * Literally, the multiplicative group of the prime field $$F_p$$
 * The group which as a set is nonzero congruence classes mod $$p$$, with multiplication coming from integer multiplication

The multiplicative group of a prime field, as an abstract group, is a cyclic group of order $$p-1$$. However, there is no direct procedure to find a generator for this multiplicative group; even given a generator, constructing a bijection between this multiplicative group and the additive group modulo $$p - 1$$ is a hard task.

The computational way of viewing this is that the multiplicative group of a prime field is a black-box cyclic group, with the multiplicative structure being the encoding. The problem of finding a generator is termed the primitive root-finding problem and the problem of constructing an explicit bijection with an additive group of order $$p-1$$ is termed the discrete logarithm problem.