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Chaotic signal transmission systems are often claimed to be secure by itself. Using a simple example it is shown, that this is not true and that exact design criteria have to be set up before starting the design of a chaotic encryption system. Then, beginning with statistical design objectives an information encryption system is systematically designed. The structure design leads to a controlled filter structure with overflow nonlinearity, the parameter design has to assure chaotic behaviour and mixing properties of the encoded signal. This defines the limits for the choice of the parameter set representing the key for the encryption. After developing the system structure the system is realized by electronic circuitry. Discrete and IC versions of the solution are presented. In order to prove that the system meets the design requirements experimental results are provided. It can be shown that in a n-th order system the statistical characteristics up to the n-th order of the output signal will not be affected by the input signal. The paper closes with some security estimates for the designed system. [ABSTRACT FROM AUTHOR]