Secure data deduplication has received great attention from both academic and industrial societies. It is highly motivated for cloud service providers to delete duplicated data from their storage. Plaintext data deduplication is a simple problem, but users tend to encrypt their data with their own keys before uploading them to the cloud, which makes it difficult to perform cross user deduplication. Most current solutions to the problem rely on trusted third parties. In this study, an encrypted data deduplication scheme is presented based on an offline key distribution protocol. A bilinear mapping is constructed to verify whether different encrypted data originate from the same plaintext. Secure key storage and key delivery is achieved by using the broadcast encryption technique. An original uploading user of some data can validate successive uploading users via the cloud service provider, and the data encryption key can be distributed in an offline manner. The cloud service provider can accomplish encrypted data deduplication with no online interaction with any trusted third party. The security of the proposed scheme is analyzed and proven. Simulation experiments show that the scheme is efficient and applicable.