Abstract: Recommendation systems require extensive user data for computations, posing a risk to user privacy. While differential privacy techniques have been used to protect user privacy, in untrusted server scenarios, existing methods suffer from reduced recommendation effectiveness due to excessive noise injection. To address this issue, we propose a differential privacy matrix factorization recommendation algorithm that incorporates a shuffler to leverage the privacy amplification effect of shuffling operations for noise reduction. Additionally, we address the problem of recommendation performance degradation caused by data sparsity by adding noise to the top k gradients locally, thus achieving a better balance between privacy protection and data utility optimization. Theoretical and experimental results confirm that this algorithm not only effectively enhances privacy protection but also yields excellent recommendation results, demonstrating its promising application potential.