With the exponential growth of multimedia data, especially images, in cloud storage, deduplication has become an essential technique to reduce storage and communication overheads. However, ensuring the confidentiality and security of deduplicated encrypted images presents significant challenges, particularly regarding side-channel attacks and the overhead associated with key transfer. This paper introduces SEDDS (Secure Encrypted Data Deduplication System), a novel framework that integrates adaptive MSB reversible data hiding with traditional deduplication techniques to address these challenges. By embedding key transfer auxiliary information directly into the encrypted images, SEDDS eliminates the need for additional communication and storage overhead for auxiliary information. This method also ensures indistinguishable responses to deduplication requests, thereby resisting side-channel attacks. Our security analysis and experimental results demonstrate that SEDDS not only enhances security against side-channel attacks but also significantly reduces communication and storage overheads compared to existing schemes.