This paper presents a fast encryption algorithm for speech signals using the Arnold 3D and the Tent Map chaotic transformations. Arnold 3D chaotic map is known for the property of simultaneously combining pixel scrambling with changing their value in the process of image encryption. The aim of the architecture was to obtain a simple, robust algorithm with short encryption and decryption times, as well as resistant to attacks. All these features make it suitable for real-time communication. The algorithm consists in segmenting the speech signal, then transforming this frame into a cubic three-dimensional structure of samples. The samples are inserted sequentially in vertical slices. Arnold 3D transformation is applied to this structure on horizontal slices, each slice having its own encryption key generated by a Tent Map transformation.
The novelty of this work is the statistical perspective of the cryptanalyst being able to perform a chosen plaintext attack on a private communication scheme involving chaos-based algorithms. The attacker finds himself in the position of analyzing the pseudo-random matrix that was used for encryption. The contribution is done in the context of the well-known fields of secret-key cryptology and that of wavelet packet decomposition of images. The analysis is exemplified on the thoroughly investigated, in the existing literature, simplest chaotic system, the logistic map. Kolmogorov-Smirnov tests, histogram testing, autocorrelation functions and nonlinear singular value decomposition are used. In addition, a new enciphering wavelet-based algorithm is proposed and analyzed.
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