Grid computing, as a distributed computing model, stands for the new kind of systems that pools heterogeneous computational resources, such as computers, storage space, sensors, application software, and experiment data. When a user wants to request some computing and data resources, the grid can seamlessly, transparently and dynamically supply them. The security issue has become an important concern of grid computing. To prevent the grid resources from being illegally visited, the strong mutual authentication is needed for user and server. In recent periods, many password-based user authentication schemes are proposed for solving the authentication issue. However, most of them are not ideal for grid computing, since they do not provide the strong mutual authentication. It is proposed to introduce an efficient user Cyclic Shift Transposition Algorithm (CSTA) scheme and a model for secure routing mechanism of sharing messages between source and destination in grid computing by adding information about sender and preserves the message content, which prevents not only known attacks but also maintains the integrity of data. This efficient method is implemented over text data. This model dynamically reorders the frequency of the input symbols according to the coupled cyclic shift system.All text is coded during initialization. The output from the engine is in the form of variable size words and the individual bit output corresponding to the inserted symbols cannot be determined thus highly confidential.