[Jeyaseelan et al., 3(4): April, 2014] ISSN: 2277-9655 Impact Factor: 1.852 http: // www.ijesrt.com(C)International Journal of Engineering Sciences & Research Technology [2066-2071] IJESRT INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY Resolving large and Complex Matrix Factorization Problem using Cloud Platform as a Service R.Jeyaseelan *1 , N.Pandeeswari 2 , Dr. P.Ganeshkumar 3 *1 PG Scholar, 2 Assistant Professor, 3 Professor, Department of Information Technology, PSNA College of Engineering and Technology, Dindigul, India Jai.seelan98@gmail.com Abstract Cloud computing enables the resource constrained clients lacks economically, to use the huge computational power of cloud resources to outsource their complex computational tasks. However, outsourcing original input to the public cloud causes severe anxiety over security risks. The input/output privacy has to be maintained and also, proof has to be generated to verify the result against the malicious cloud server.The matrix factorization (MF) which requires enormous amount of resources to complete its task; is pretty common in engineering and economics computational task such as text mining and analysis. The proposed scheme is motivated to design a secure, resilient and efficient outsourcing of MF to the public cloud server. The concept behind defending the input matrix is by applying the transposition and permutations on the original matrix to acquire encrypted matrix. Then, the result returned from the cloud is decrypted and proof verification is done to ensure the correctness of cloud server. This paper exhibits that the how securely and efficiently proposed protocol outsources the MF problem onto the cloud and then verifying the result against malicious cloud server. Extensive theoretical and experimental analysis shows that this protocol is extremely efficient and widely applicable for practical use. Keywords: Cloud computing, matrix factorization, robust cheating resistance, secure outsourcing, Monte carlo verification Introduction Cloud computing is the recent innovative technology is defined as [1] providing on demand network access to a large pool of computing platform deployed with greater efficiency and little management overhead. With the efficient computing paradigm, the clients’ lacks due to the limited computational resources are encouraged to utilize the cloud computing utility. Instead of setting up their own computing platform with huge amount of resources, the clients can utilize the computing platform provided through one of the cloud services, Platform as a service (PaaS) on pay per use manner. Despite with the beneficial services, outsourcing client’s original information to the malicious cloud server may bring security risks and challenges [1]. Before outsourcing original information to the public cloud, the original information has to be transferred to its encrypted version. Since the large scale matrix factorization problem is computationally complex [3] to solve with restricted amount of resources. The proposed paper aims to outsource the MF problem into the public cloud to use the on demand computing platform with greater amount of resources. And also, it is significant to ensure the input/output privacy. The original input matrix protected by doing transposition and permutations. Then the encrypted matrix is forwarded to the cloud server. The result come back from the cloud server is decrypted at client side. Due to the openness of cloud computing platform, result produced by cloud server is not yet ensured as correct. Rather, the computation inside cloud is not transparent [4] and no guarantee to the quality of the computational result. In addition, some accidental reasons such as [1] software bugs and hardware failures may produce false computation result. Consequently, to necessitate the correctness of the computing utility, it is optimal to ensure the correctness of result. The proposed work contributes to design a protocol which is secure, robust and efficient to outsource the MF problem to the public cloud. This protocol design has four phases specified in order namely key generation, MF encryption, MF decryption, and result verification. Key generation phase is used to generate a secret key for every