Residue number system which was inspired by the Chinese remainder theorem provides a method for using groups of smaller numbers to represent large integers. Although cryptographic algorithms based on radix or decimal arithmetic have their advantages, direct sum of smaller rings properties-based algorithms offers better benefits. In this paper, the application of RNS number systems successfully utilized in text security for exponential cipher. RNS-based cipher systems exhibit properties that increase computation speed, reduce the time complexity, and make the system immune to known plain text attacks and algebraic attacks. In addition to this, the characteristics of exponential stream cipher systems, the key generation, and residue number system-based encryption and decryption are discussed in this paper.