What is the devil's authority?
The devil obviously had access to Adam and Eve in the garden of Eden. Scripture does not tell us why God allowed this. One theory that makes sense involves mankind being allowed to judge the devil, possibly after the devil complained that God was not just or fair in condemning him. First Corinthians 6:3 does say that Christians will judge angels — and the devil is a fallen angel. If this theory is correct, God would have to allow the devil access to influence mankind, or be seen as unfair by all.
The devil gained a certain amount of control over mankind by Adam’s disobedience, which plunged Adam and all his descendants into spiritual death.
At the time of the temptation of Christ, recorded in Luke 4, the devil obviously had a great amount of authority in the world system.
LUKE 4:4-7 NKJ
4 But Jesus answered him, saying, “It is written, ‘Man shall not live by bread alone, but by every word of God.’ ”
5 Then the devil, taking Him up on a high mountain, showed Him all the kingdoms of the world in a moment of time.
6 And the devil said to Him, “All this authority I will give You, and their glory; for this has been delivered to me, and I give it to whomever I wish.
7 “Therefore, if You will worship before me, all will be Yours.” ...