In the paper we propose a method of constructing cryptosystems, utilizing a
nonpredictability property of discrete chaotic systems. We point out the r
equirements for such systems to ensure their security. The presented algori
thms of encryption and decryption are based on multiple iteration of a cert
ain dynamical chaotic system coming from gas dynamics models. A plaintext m
essage specifies a part of the initial condition of the system (a particle'
s initial position). A secret key specifies the remaining part of initial c
ondition (the particle's initial angle) as well as a sequence of discrete c
hoices of the pre-images in the encryption procedure. We also discuss probl
ems connected with the practical realization of such chaotic cryptosystems.
Finally we demonstrate numerical experiments illustrating the basic proper
ties of the proposed cryptosystem.