Compression of data has become a worldwide phenomenon during the past few decades for rea- son of achieving savings in band-width (BW) and hence makes it cost effective. The widespread practice of encryption of data has generated interest for many decades and it mainly aims at pro- tection of data. Combining these two apparently contrary processes (in terms of BW) is quite challenging. Whereas the research on concurrent data compression and data protection (encryp- tion) is still on, the methodology adopted by the author is unique and quite new. The most impor- tant aim of data compression technique is the need for curtailing the data storage and communi- cation expenses. The source message (long) is converted to a codeword (small). The key objec- tive of data encryption is to guard the integrity of data if it is intercepted by an eavesdropper. The plaintext is transformed in to ciphertext using an encryption key or keys. Combining the processes of compression and encryption together must be done in this order, that is, compres- sion followed by encryption because all compression techniques heavily rely on the redundancies inherently part of a regular text or speech. The speech compression has been achieved using Lempel-Ziv 78 algorithm and a new algorithm for encryption/decryption, named ―The Random- One, abbreviated as TR-1‖ is developed during this study and is thoroughly tested. The results obtained are quite encouraging. Firstly, contrary to the use of conventional methods the algo- rithm developed in this study does not use exclusive-OR (XOR) operation in Permutation (P) and Distribution (D) boxes for producing ciphertext from the plaintext. In this scheme pseudo ran- dom number (PRN) is used only to deceive the intruder by adding more confusion (meaning compared to the confusion due to the use of some tested algorithms used in this research). In fact only the sender of information and the intended recipient (not intruders) should be aware of the 44 bit positions filled by the PRN in a 128 word. The intended recipient discards these during deciphering process at the right time (these are disposed of before performing the inverse map- ping in the P-Box). Secondly, protection against attacks is further ensured by using two supple- mentary keys, one for the P-Box, and another for the D-box. In addition the routine key-set of the N selected algorithms further enhances the security. In a small set-up, the distribution of key-set can be mutually agreed upon by the users; but in a large set-up, the distribution of these sets can be accomplished using standard key distribution techniques. Moreover, the proposed algorithm- - also differs from the other methods currently in use due to deployment of a ―sentinel marker”; which is not adopted by other algorithms and this proposal is purely the brain child of the author. The sentinel marker is part of the secret key which is pre-decided and predetermined by the sender and the intended recipient of the information. Twenty bits (out of a total of 128) are used for the sentinel marker which amounts to 2^20 = 1,048,576 possibilities combined with 2^44 = 17.6 trillion possibilities of the ciphertext produced by the PRN. The job for the cryptanalyst to break this cipher becomes formidable and a fool-proof security of data is ensured.