How can I show the one I love that they can trust me again?

The relationship between my boyfriend and I is hard to describe. We’ve gone through many hard times, but love eachother and have always pulled through and we make eachother very happy. Two weeks ago, we decided to break up because the past kept coming back to us both. I was very upset though because my love was still very strong, but I knew it was over and that I needed to move on. During the time we broke up, I ended up getting together physically with another man. My boyfriend and I continued to talk and sorted out our problems together, and were ready to try again because we truly believed we were right for eachother, but I felt that he deserved to know what had happened with the other man. He appreciated that I had told him, but continously kept pushing me for every detail possible. I didn’t feel it necessary that he had to know every detail, because I know that would just hurt him and I didn’t want to lose him. Out of fear of losing him forever, I lied and told him there was nothing I hadn’t told him, when there were in fact some ‘details’ that he did not know. Eventually he found out I had lied, and now he does not trust me. I know I am not a liar, and that I did it out of fear of losing him, and to prevent him some hurt, but I know it was still wrong to lie. I was always against lying. I know I would never lie to him again and that he could completely trust me, but he doesn’t know if he can forgive me ever. I’ve explained to him why I lied and told him many times that I won’t lie again, but I know words aren’t of much value to him right now. How can I show him that he can trust me again? Someone please give me some advice. I don’t want to lose him.