I wish to encrypt an image using Logistic map. A Logistic map can be specified with the Equation:

x_{n+1} = r*x_n (1-x_n).

Now, according to the Kerckhoff principle, the entire system's security is dependent on the key. Perfect chaos can be achieved with a fixed control parameter (r) and initial condition (x_0). How can the authors identify the initial conditions (x_0) and control parameter(r) as the secret key? The parameters must be accessible to the public in order to generate "perfect chaotic values", which will be used to encrypt the image. However, if the parameter and the initial condition are known, any attacker can reproduce the "perfect chaotic values." Can anyone throw some light in this concept? What am I missing?