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A new original method of information processing and secure communications based on coding of the alphabet symbols by means of stabilized cycles of certain one-dimensional dynamical systems family is proposed.Stabilization of the prescribed cycles is ensured through periodic parametric perturbations.The foundation of the proposed method is ciphering by the one-to one correspondence between periods of such cycles and certain alphabet symbols.It is shown that for some maps the perturbations which lead to the stabilization of cycles of given period,form some domain in the parametric space.This fact is used for coding of identical symbols via the random selection of parameters from this domain,that means that the probability of deciphering of the transmitting information by an external observer is zero.Analytic estimations of the admissible noise level in the communication channel and the randomness degree of transmitting signals are made.Several variants of the ciphered sequences are presented.The eryptostability of the proposed method is estimated.