Data compression and encryption are essential features when digital data is stored or transmitted over insecure channels. Usually, we apply two sequential operations: first, we apply data compression to save disk space and to reduce transmission costs, and second, data encryption to provide confidentiality. This solution works fine for most applications, but we have to execute two expensive operations, and if we want to access data, we must first decipher and then decompress the ciphertext to restore information. In this work we propose algorithms that achieve both compressed and encrypted data. The first contribution of this thesis is the algorithm ADDNULLS - Selective Addition of Nulls. This algorithm uses steganographic technique to hide the real symbols of the encoded text within fake ones. It is based on selective insertion of a variable number of null symbols after the real ones. It is shown that coding and decoding rates loss are small. The disadvantage is ciphertext expansion. The second contribution of this thesis is the algorithm HHC - Homophonic- Canonic Huffman. This algorithm creates a new homophonic tree based upon the original canonical Huffman tree for the input text. It is shown the results of the experiments. Adding security has not significantly decreased performance. The third contribution of this thesis is the algorithm RHUFF - Randomized Huffman. This algorithm is a variant of Huffman codes that defines a crypto-compression algorithm that randomizes output. The goal is to generate random ciphertexts as output to obscure the redundancies in the plaintext (confusion). The algorithm uses homophonic substitution, canonical Huffman codes and a secret key for ciphering. The secret key is based on an initial permutation function, which dissipates the redundancy of the plaintext over the ciphertext (diffusion). The fourth contribution of this thesis is the algorithm HSPC2 - Homophonic Substitution Prefix Codes with 2 homophones. It is proposed a provably secure algorithm by using a homophonic substitution algorithm and a key. In the encoding process, the HSPC2 function appends a one bit suffx to some codes. A secret key and a homophonic rate parameters control this appending. It is shown that breaking HSPC2 is an NP-Complete problem.