Two approaches are presented to stream cipher utilizing a peculiar dynamical system called as composite discrete chaotic dynamical system (for short, composite system), which consists of two chaotic dynamical systems. The secret keys are the initial state of the chaotic dynamical systems, and the plaintext is used as its composite sequence that decides the choice of iterating function in the iterating process. Because of sensitivity of the composite system to initial conditions and randomness in the iterating process, the approach mingles secret keys with plaintext when using the composite system to produce ciphertext. Therefore they hold very complex and sensitive nonlinear relations. The algorithm is also provided with uniform distributing ciphertext. These peculiarities prevent ciphertext to leak the information of plaintext and secret key and make the security of the algorithms not depend on the complexity of the ciphertext.