Computing multiplicative order and primitive root in finite cyclic group

Multiplicative order of an element a of Group g is the least positive integer n such that aⁿ = e, where e is the identity element of G. If the order of an element is equal to |G|, it is called generator or primitive root. This paper describes the algorithms for computing multiplicative order and primitive root in ℤ_p*, we also present a logarithmic improvement over classical algorithms.