Public key cryptosystem based on Pell's Equation with Jacobi symbol

Protection of data is the utmost thing for any company related to digital information. There are several malicious methods adapted, based on the priority of demand of that piece of information. There are several cryptosystems implementing various algorithms. In this paper a cryptosystem based on Pell's Equations proposed with Jacobi Symbol. And an efficient implementation of RSA algorithm and Pell's Equation with Jacobi Symbol using GMP library from GNU is done. An analysis based on the changes in the performance of the algorithm by changing the number of bits of message and keys is done.