Not so. Pilate's authority was simply that of his office as Procurator of Judea. Normal, earthly authority given to him from above, which Jesus had already recognised as legitimate (Render unto Caesar ...) and which St. Paul would later recognise as legitimate when he notes, among other things, that Kings "do not wield the sword in vain".
"Not so. Pilate's authority was simply that ..."
So your contention Jesus was simply in the chain of authority, so to speak.
Here's why I don't buy that.
"Then Jesus said to him, "Put your sword back into its place. For all who take the sword will perish by the sword. Do you think that I cannot appeal to my Father, and he will at once send me more than twelve legions of angels? But how then should the Scriptures be fulfilled, that it must be so?"
What are suggesting - that Pilate had some sort of legitimate authority over Jesus, would make Jesus be claiming rebellious and illegal authority to protect himself in the above passage - something that, according to Jesus, God was more than willing to do should he ask it.
"St. Paul would later recognise as legitimate when he notes, among other things, that Kings "do not wield the sword in vain"."
Yes. Paul recognizes duly constituted authority - but make no mistake, he also clearly teaches that the world is in the grip of devil. He is the prince of this age, or as John says...
"We know that we are from God, and the whole world lies in the power of the evil one." - 1 John 5