Thwarting cryptanalytic attacks based on the correlation function

Many studies analyze the encrypted transmission using the synchronization of chaotic signals. This requires the exchange of an analog synchronization signal, which almost always is a state of the chaotic generator. However, very few different chaotic structures are used for this purpose, still. The uniqueness of their dynamics allows the identification of these structures by simple autocorrelation. In order to thwart all cryptanalytic attacks based on the identification of this dynamics, we propose a numerical method without memory in order to reversibly destroy the shape of the transmitted signal. After analog-to-digital conversion of the synchronization signal, we apply permutations of the weights of its bits to each binary word. These permutations significantly change the shape of the transmitted signal, increasing its versatility and spreading its spectrum. If the message is simply added to the synchronization signal, being the easiest to decrypt, it undergoes the same transformation. It is therefore extremely difficult to detect the message in the transmitted signal by using a temporal analysis, as well as a frequency one. The present work illustrates the proposed method for the chaotic Colpitts oscillator. Nevertheless, the algorithm does not depend on the chosen chaotic generator. Finally, by only increasing the size of the permutation matrix, the complexity of the change in the waveform is increased in a factorial way.