Otherwise, we would be doing something for our salvation. Also, a quick note on Judas. Although, we cannot be sure of anyone's faith, Judas' repentance would seem to be an outward sign that would point towards the possibility of having faith. There are two things that define repentance and one thing that follows repentance naturally as a fruit. The two defining things are contrition and faith.
Contrition is sorrow for sin.
It is sorrow before God and to God that one has sinned against God. Faith refers to faith in Jesus Christ for forgiveness. It is trust that God has forgiven all sin and all sinners and my sin and me, personally. Therefore, I am justified by faith. So, in the context of your question.