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Deduplication eliminates duplicated data copies and reduces storage costs of cloud service providers. However, deduplication of encrypted data is difficult. Current solutions rely heavily on trusted third parties, and do not address the popularity of data, resulting in unsatisfying security and efficiency. A secure encrypted data deduplication scheme based on data popularity is proposed. Check tags are calculated via bilinear mapping to determine whether different encrypted data originate from the same plaintext. Ciphertext policy attribute-based encryption is applied to protect the tags. A secure key delivery scheme is designed to pass the data encryption key from an initial data uploader to subsequent uploaders via the cloud server in an offline manner. The cloud server can perform deduplication without the assistance of any online third party. Security analysis and simulation experiments are provided, proving the practicability and efficiency of the proposed scheme.