We both lied to each other

Me and my boyfriend both admitted to lying to each other and we both broke our trust for one another. I told a lie in order to protect his feelings and myself, and he snooped through my phone a couple of times. I feel awful for lying to him and know that I should have told the truth immediately. He didn’t really apologise for what he did and only told me to understand that he was curious about my past. Now I feel like he doesn’t respect my privacy and that I can’t trust him to keep his promises. And he doesn’t fully believe me when I promise things. How do we fix this and build up the trust again?