With the advent of cloud computing, users are increasingly choosing to store their data on cloud. As a result, data integrity and availability have emerged as key concerns for data owners. Users expect to store multiple copies of their data to cloud and ensure the integrity of these data copies. Currently, numerous multi-copy cloud storage auditing schemes have been proposed. However, most of them depend on public key infrastructure, identity-based cryptography, or certificateless cryptography. These schemes encounter challenges such as complicated certificate management, key escrow, or the necessity for a secure channel for distributing keys, respectively. Furthermore, most of them are not resilient to copy-summation attack. To address the above problems, we propose a certificate-based multi-copy cloud storage auditing scheme supporting data dynamics. We design a novel dynamic structure named Leaves Merkle hash tree (LMHT) to achieve multi-copy dynamic updates. Different from traditional Merkle hash trees, LMHT has significant advantages in data deletion. In addition, the proposed scheme can resist copy-summation attack, in which cloud cannot pass the verification if it only stores summation of all copies without storing data blocks’ all copies. Security analysis and performance evaluation demonstrate that the proposed scheme is secure and efficient.