Spectral space as a method for data crypto protection using the fast Fourier transform

Abstract

The article proposes to solve the problem of real-time application (on-line) of asymmetric bit-by-bit (flow or phoneme block, 32-, 64-,..., n-bits block) encryption of the linear and / or non-linear formants of the spectrum lines of Fast Fourier Transform (FFT) as an indirect analogue of a voice message. For this, modernized RSA-m algorithms are used and the spectrum of the voice message in the form of linear formants of number theory, while maintaining the high level of cryptographic resistance inherent of the RSA algorithm. The peculiarity of these algorithms consists in the fact that different lengths of cryptographic keys are used, which are changed with a sufficient frequency, depending on the required level of cryptographic resistance. This feature of the algorithms implements statistically independent encoding of the original message, by encrypting the adequate formants of the original message, i.e. a process characterized by a reduction (compression) of the amount of initial information and its redundancy, as well as an increase of its entropy (the average amount of information per character, phoneme or discrete (n-bit output from the ADC), because in a compressed context, statistically frequent sounds, letters, words, phonemes and even discrete, will be absent, which will significantly complicate the decryption (cryptanalysis) of the message.