This research study proposes Hybrid Encryption System using new public key algorithm and private key algorithm. A hybrid cryptosystem is one which combines the convenience of a public-key cryptosystem with the efficiency of a symmetrickey cryptosystem. Here, we propose a provably two way secured data encryption system, which addresses the concerns of user’s privacy, authentication and accuracy. This system has two different encryption algorithms have been used both in the Encryption and decryption sequence. One is public key cryptography based on linear block cipher another one is private key cryptography based on simple symmetric algorithm. This cryptography algorithm provides more security as well as authentication comparing to other existing hybrid algorithm.