Parallel Algorithm for Finding Inverse of a Matrix and its Application in Message Sharing (Coding Theory)

A parallel algorithm for finding the inverse of the matrix using Gauss Jordan method in OpenMP. The Gauss Jordan method has been chosen for this project because it provides a direct method for obtaining inverse matrix and requires approx. 50% fewer operations unlike other methods. Hence forth it is suitable for massive parallelization. Then, authors have analyzed the parallel algorithm for computing the inverse of the matrix and compared it with its perspective sequential algorithm in terms of run time, speed-up and efficiency. Further, the obtained result is used to propose a new method of Message Sharing (called Coding Theory). The proposed method is simple and has a great potential to be applied to other situation where the exchange of messages is done confidentially such as in military operation, banking transactions etc. General Terms Matrix Inversion, Security, Digital Image Processing