Using families of orthogonal functions for coding messages in a chaotic masking scheme
Keywords:
chaotic masking, orthogonal functions, hidden transmission of messages, differential chaos shift keyingAbstract
Introduction: Chaotic masking of messages is used for hidden data transfer over a communication channel. The existing chaotic
masking schemes require a sophisticated system to coordinate the chaotic generators. These systems are not stable in the case of a
noisy communication channel. One of the ways to solve this problem is using coding algorithms which allow you to extract messages
from a noisy container without any extra information about the chaotic generator. Purpose: Development of a chaotic masking scheme
which does not need the noise generators to be coordinated and which is immune to transfer over noisy channels. Methods: The signal
is represented as a superposition of orthogonal functions with weighting coefficients determined by the bits in the message being
transferred. A message is extracted from the chaotic signal by calculating its projection on a family of orthogonal functions. Results:
Based on the proposed method, a chaotic masking scheme is constructed for hidden data transfer. It does not need the chaotic generators
of the transmitter and receiver to be synchronized. Messages are concealed by mixing the useful and chaotic signals. The useful signal
can be extracted because the functions used for the coding are orthogonal. It is assumed that noise projection on orthogonal functions is
very small. To calculate this projection, digital integration was used. A computer experiment was performed for two families of simple
trigonometric functions. It showed that the proposed scheme allows you to recover the signal with a high precision for noise-to-signal
ratio 38 dB (the probability of a correct byte transfer is more than 0.95). The success of recovering strongly depends on the digital
integration precision. To increase the allowable noise level, you need to use more precise integration methods. Practical relevance: The
results of the study can be used for developing systems with hidden message transmission. The proposed approach allows you to improve
the stability of a chaotic masking scheme to the noise in communication channels.