This research work proposes two techniques of joint compression and encryption using Shanon Fano Elias coding and Arithmetic coding respectively. The first scheme proposed is called Adaptive Shannon-Fano-Elias code where it has been observed that the complexity of attacks is exponential in m, where m is the length of the string being compressed. Since mis usually very large (> 220 ), the security of our scheme is very high. The main reason why our scheme's security depends on m is the fact that all attacks require the ciphertext to be scanned from left to right. The algorithm proposed does not compromise in the compression ratio produced by normal Shannon Fano Elia coding. The second scheme proposed uses Arithmetic coding as the compression algorithm as Arithmetic coding is one of the optimal compression techniques that can be used in various applications. The algorithm proposed is proved to be secure under an assumption that the attacker would have access to an algorithm which could decrypt any given message without the knowledge of the key. i