The problem of nonlinear substitution generation (S-boxes) is investigated in many related works in symmetric key cryptography. In particular, the strength of symmetric ciphers to linear cryptanalysis is directly related to the nonlinearity of substitution. In addition to being highly nonlinear, S-boxes must be random, i.e., must not contain hidden mathematical constructs that facilitate algebraic cryptanalysis. The generation of such substitutions is a complex combinatorial optimization problem. Probabilistic algorithms are used to solve it, for instance the simulated annealing algorithm, which is well-fitted to a discrete search space. We propose a new cost function based on Walsh–Hadamard spectrum computation, and investigate the search efficiency of S-boxes using a simulated annealing algorithm. For this purpose, we conduct numerous experiments with different input parameters: initial temperature, cooling coefficient, number of internal and external loops. As the results of the research show, applying the new cost function allows for the rapid generation of nonlinear substitutions. To find 8-bit bijective S-boxes with nonlinearity 104, we need about 83,000 iterations. At the same time, the probability of finding the target result is 100%.
Direct spread spectrum technology is traditionally used in radio communication systems with multiple access, for example, in CDMA standards, in global satellite navigation systems, in Wi-Fi network wireless protocols, etc. It ensures high security and reliability of information transfer. In addition, spread spectrum technology provides the transmitted signals with a noise-like appearance, thus hiding the semantic content of the messages. We researched this technology for other implementations. The purpose of our study was to investigate new technologies for hiding data in multimedia files. In particular, we investigated the direct spread spectrum in the context of the development of methods for hiding data in audio containers. We considered various spreading sequences (chip codes) and also explored their use for hiding information in audio files. We conducted experimental studies and estimated the bit error rate (BER) in the recovered data. The article also evaluates the distortion of an audio container by the peak signal-to-noise ratio (PSNR). The results of our research enable us to find out which method of forming chip codes gives a lower BER with equal PSNR. We provide recommendations on the formation of spreading sequences to reliably and safely hide informational messages in audio files.
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