I ran away from home and now I live at my friends house
What caused you to want to run away from home?
My parents were encroaching on my privacy
Running away from home because your parents weren't giving you enough privacy is a bad idea. Your parents are going to be worried about you. If you don't like how your parents are treating you then you should discuss it with them, not leave.
They had no right to read my diary.
Running away from home is a bad idea. What would be better is if you discussed how you felt with your parents instead of simply showing them you are upset by your actions. While it is wrong for them to read your diary, maybe this was a way of them showing you that they want to know more about your life.