Combined formаtion of a cryptographic key using synchronized artificial neural networks

А combined method for forming a cryptographic key is proposed in the article. The proposed combined formation consists of two stages: the formation of partially coinciding binary sequences using synchronized artificial neural networks and the elimination of mismatched bits by open comparison of the parities of bit pairs. In this paper, possible vulnerabilities of the basic method of forming a cryptographic key using synchronized artificial neural networks are considered, their danger is assessed, and a correction of the method is proposed to ensure the required confidentiality of the generated shared secret. At the first stage, a deferred brute-force attack is considered. To neutralize this attack, it is proposed to use the convolution function of the results of several independent synchronizations. As a convolution function, the bitwise addition modulo 2 of the vectors of the weights of the networks is used. Due to the correction of the first stage of the basic algorithm, the amount of deferred search exponentially increases, and frequency analysis of binary sequences also becomes ineffective. At the second stage, an attack based on the knowledge of pair parities is considered, taking into account the proposed method for correcting the first stage. The analysis of the influence of network parameters on the process of eliminating the bit mismatch at the second stage is carried out. Statistical modeling of this analysis has been performed. The results obtained showed that the cryptanalyst could not uniquely distinguish the values of the remaining bits. The proposed combined method makes it possible to increase the confidentiality of the generated shared secret and significantly reduce the number of information exchanges in comparison with the Neural key generation technology.