Data security has turned-out to be a very important aspect in recent years due to drastic progress in the use of internet, data is frequently transferred from one place to another especially with the use of internet in recent years. Sensitive information can be shared through internet but this information sharing is vulnerable to certain attacks. Cryptography was introduced to solve this problem. Cryptography is the art of achieving security by encoding the plaintext message to cipher text. Many ciphers have been developed to provide data security, such as Caesar cipher, Hill cipher, Vigenere cipher, Rail fencing cipher, Playfair cipher and so on, but all the conventional encryption techniques have proved to be weak and amenable to attack even by use of brute force and traditional cryptanalysis. In this work three of those existed ciphers will be considered (i.e. Caesar cipher, Hill cipher and RSA Algorithm) and their weaknesses will be proved. The three ciphers will be measured as functions (bijection) and idea of composition of functions will be used to combine and compose the functions so as to provide an improved encryption technique (hybrid cipher system) by combining RSA Algorithm together with Shifting and Hill ciphers