Cloud computing has become a reality which is capable of enabling general public and organizations to make use of huge computational resources without capital investment in pay per use fashion. This new paradigm allows customers who have no much computational resources to outsource their expensive computational workloads to cloud and get the benefits of its storage, servers, networking and other facilities. Thus cloud computing has unlimited possibilities as one can feel world class infrastructure and facilities in her own computer sans investment. Though the provision to outsource computationally expensive workloads to cloud, there is concern about security that make people think before using cloud for this purpose. This is because basically Internet and associated infrastructure is conceived as untrusted. Though cloud service providers take care of security customer have their own concerns with respect to protection of their sensitive data. Therefore, it is required to have secure mechanism to protect data of customers and also ensure that the results are properly validated. This will enable customers to outsource their works fearlessly. The complete communication should take place in encrypted format. This is practically a challenging problem. This paper focuses on the Linear programming computations that take place over cloud with complete security. The proposed system takes care of data security while it is in transit and also has mechanisms to support verification of data for correctness. The empirical results reveal that the proposed system is practical and can be used in the real world systems. It is also found that the result verification of the system is computationally efficient does not incur additional cost.