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Cloud computing becomes the next generation architecture of IT Enterprise. Clouds are massively complex systems. They can be reduced to simple primitives, that are replicated thousands of times, and common functional units. The complexity of cloud computing create many issues related to security as well as all aspects of Cloud computing. One of the most important issues is data security. Clouds typically have a single security architecture but has many customers with different demands. The main focus of the proposed work is the data storage security in the cloud and the desktop. Generally, Data security is an important factor for both cloud computing and traditional desktop applications. This is to obtain the highest possible level of privacy. Modern Encryption algorithms play the main role in data security of cloud computing. We present an evaluation for selected eight modern encryption techniques namely: RC4, RC6, MARS, AES, DES, 3DES, Two-Fish, and Blowfish at two independent platforms namely; desktop computer and Amazon EC2 Micro Instance cloud computing environment. The evaluation has performed for those encryption algorithms according to randomness testing by using NIST statistical testing in the cloud computing environment. This evaluation uses Pseudo Random Number Generator (PRNG) to determine the most suitable technique and analysis the performance of selected modern encryption techniques. Cryptography algorithms are implemented using Java Cryptography Extensions (JCE). Simulation results are shown to demonstrate the effectiveness of each algorithm.