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A public key system is a form of crypto system in which the encryption and decryption are performed using different keys, one is public and other one is private. The mostly used public key systems like RSA, knapsack system, Elliptical curve etc are based on a single hard problem like factoring or discrete logarithm. Even if these algorithms are very secure now, in future the situation can be changed and someone can solve the single hard problem easily. In this work, a new paired cipher text public key System based on RSA is designed, which incorporates two hard mathematical problems (Both Discrete logarithms and Factoring) to make the algorithm too secure.