Implicit feedback data has become the primary choice for building recommendation models due to its abundance and ease for collection in the real world. The strong generalization capability and high computational efficiency of matrix factorization make it one of the principal models for constructing recommender systems. Recommenders have to collect vast amounts of user data for model training, which poses a significant threat to user privacy. Most of the current privacy enhancing recommendation systems mainly focus on explicit feedback data, and there are limited studies dedicated to the privacy protection of implicit recommender. To bridge the existing research gap, this paper designs a distributed differentially private matrix factorization for implicit feedback data in scenarios where the recommender is not trusted. Our mechanism not only eliminates the assumption of a trusted recommender, but also achieves the same accuracy as CDP-based privacy-preserving MF model. We prove that our mechanism satisfies$(\epsilon,\delta)$-CDP. The experimental results on three public datasets confirm that the proposed mechanism can achieve high recommendation quality.