MPI is a de facto standard for message passing for high performance parallel, as well as, for distributed computing environment. The static and homogenous model of MPI is not compatible with the dynamic and heterogeneous Grid environment. There are not many implementations which offer message passing over Internet and Grids. P2P-MPI and A-JUMP are MPI implementations, which provide both point-to-point and collective data operations over Internet using Java. However, none of these MPI implementations are categorized as a secure message passing implementation. In these MPI implementations security is overlooked to avoid performance degradation. Security becomes a fundamental concern when considering message passing over Internet, and should be accordingly addressed. Moreover, access over Internet requires authorization/authentication of resources and users along with encryption of data. In this paper, we have proposed secure message passing over Internet and Grids using A-JUMP. This paper also presents performance analysis and comparison of the proposed model with P2P-MPI and A-JUMP.