The increasing prevalence of cloud services has promoted storing data on cloud servers to facilitate data sharing, while also posing severe data security challenge. A straightforward approach is to utilize ring signatures in cloud data management to provide cloud data owner anonymity and cloud data unforgeability. Nonetheless, most ring signatures are susceptible to quantum attacks. To address this issue, researchers explore lattice-based ring signatures to enjoy quantum safety. But to our best knowledge, existing lattice-based ring signatures exhibit restricted applicability due to impractically large signature sizes and limited functionality. In this paper, we present a logarithmic-size lattice-based linkable ring signature for cloud data management. To achieve this, we introduce a generalized lattice-based Bulletproofs compression technique and apply it to scheme [AFRICACRYPT’13] to present a logarithmic-size lattice-based ring signature protocol. Building upon this protocol and our designed link label, we propose a logarithmic-size lattice-based linkable ring signature that provides user privacy, ensures cloud data unforgeability, and enables checking if multiple cloud data are from same user. Our scheme is proven to satisfy the anonymity, unforgeability, and linkability. Comprehensive evaluations demonstrate that our scheme outperforms existing state-of-the-art schemes.