With the tremendous growth of available digital data, the use of Cloud Service Providers (CSPs) are gaining more popularity, since these types of services promise to provide convenient and efficient storage services to end-users by taking advantage of a new set of benefits and savings offered by cloud technologies in terms of computational, storage, bandwidth, and transmission costs. In order to achieve savings in storage, CSPs often employ data dedplication techniques to eliminate duplicated data. However, benefits gained through these techniques have to balanced against users' privacy concerns, as these techniques typically require full access to data. In this thesis, we propose solutions for different data types (text, image and video) for secure data deduplication in cloud environments. Our schemes allow users to upload their data in a secure and efficient manner such that neither a semi-honest CSP nor a malicious user can access or compromise the security of the data. We use different image and video processing techniques, such as data compression, in order to further improve the efficiency of our proposed schemes. The security of the deduplication schemes is provided by applying suitable encryption schemes and error correcting codes. Moreover, we propose proof of storage protocols including Proof of Retrievability (POR) and Proof of Ownership (POW) so that users of cloud storage services are able to ensure that their data has been saved in the cloud without tampering or manipulation. Experimental results are provided to validate the effectiveness of the proposed schemes.