Introduction: Communication systems based on the use of dynamical chaos have a number of positive features. Dynamical chaoshas the properties of random processes, which allows systems based on it to ensure the information transmission confidentiality.However, a quantitative security assessment of such systems is a complicated problem, since the methods for evaluating cryptographicstrength are well developed only for the classical encryption algorithms. Purpose: Development of a method for quantitative estimationof confidentiality of a binary signal hidden transmission in a communication system based on a chaotic time-delay oscillator withswitchable delay time. Results: A method is proposed for estimating the confidentiality of a binary information signal transmissionin a communication system using a chaotic time-delay oscillator with switchable delay time as a transmitter. The method is based onestimating the power of the key space for the chaotic communication system under study. We have considered the cases when sometransmitter parameters are known, and the most general case when all the transmitter parameters are unknown. A communicationsystem based on dynamical chaos may have a much higher confidentiality than the classical cryptographic algorithm using a cipher witha key length of 56 bits, but is significantly inferior in terms of cryptographic strength to a cipher with a key length of 128 bits. Practicalrelevance: The proposed method allows us to obtain a quantitative estimation of confidentiality of communication systems based ondynamical chaos, and compare it with the known strength of classical cryptographic algorithms.