In this paper, The design of digital circuits for chaotic composition function which is used for the key-stream generator is studied in this work. The overall design concept and procedure due to the mathematical model of chaotic key-stream generator is to be the explained in detail, and also the discretized truth table of chaotic composition function is presented in this paper. consequently, a composition state machine based on the compositive map with connecting two types of one dimensional and two dimensional chaotic maps together is designed and presented.