Revisiting the Factorization of over Finite Fields with Applications

Algorithm 1

Algorithm for the factorization of over Fq.

	Input: odd prime power , odd integer with , and integer .
(1)	Compute the positive integer such that .
(2)	Compute and the integer such that .
(3)	Consider the following cases:(I).(i).(a). Compute .(b). Compute  and .(c). Compute (ii).(a). Compute .(b). Compute  and .(c). Compute (II).(i). Compute directly using (3)(ii). Compute