Abstract: Dynamic heterogeneous networks have become the mainstream paradigm for next-generation networks. The explosive integration of massive heterogeneous smart terminals imposes stringent requirements on encrypted data storage and privacy preservation within the cloud-edge collaborative architecture. Encrypted deduplication technology can identify and eliminate duplicate encrypted data, effectively reducing storage costs for cloud-edge environments while preserving data privacy, thus holding high practical value. However, existing encrypted deduplication schemes suffer from limitations such as vulnerability to duplicate faking attacks, high computational overhead, and heavy storage burdens on edge nodes, which fail to meet practical application demands. To address these issues, we propose SEDedup, a cross-user encrypted data deduplication scheme designed for cloud-edge storage scenarios. First, a server-aided encryption method suitable for cloud-edge storage is designed to achieve efficient and secure cross-user encrypted deduplication while effectively defending against duplicate faking attacks. Second, leveraging the temporal locality of data from heterogeneous terminals, an epoch-based duplicate data detection method is designed to achieve high-performance duplicate detection while minimizing the storage overhead on edge nodes. Finally, by incorporating generalized deduplication technology, lossless encrypted deduplication for similar heterogeneous terminal data is realized to maximize storage efficiency. Security analysis and performance evaluation demonstrate that SEDedup outperforms existing schemes in terms of performance while effectively preserving data privacy.