During the research, the analysis of the existing biometric cryptographic systems was carried out. Some methods that help to generate biometric features were considered and compared with a cryptographic key. For comparing compact vectors of biometric images and cryptographic keys, the following methods are analyzed:  designing and training of bidirectional associative memory; designing and training of single-layer and multilayer neural networks. As a result of comparative analysis of algorithms for extracting primary biometric features and comparing the generated image to a private key within the proposed authentication system, it was found that deep convolutional networks and neural network bidirectional associative memory are the most effective approach to process the data. In the research, an approach based on the integration of a biometric system and a cryptographic module was proposed, which allows using of a generated secret cryptographic key based on a biometric sample as the output of a neural network. The RSA algorithm is chosen to generate a private cryptographic key by use of convolutional neural networks and  Python libraries. The software authentication module is implemented based on the client-server architecture using various internal Python libraries. Such authentication system should be used in systems where the user data and his valuable information resources are stored or where the user can perform certain valuable operations for which a cryptographic key is required. Proposed software module based on convolutional neural networks will be a perfect tool for ensuring the confidentiality of information and for all information-communication systems, because protecting information system from unauthorized access is one of the most pressing problems. This approach as software module solves the problem of secure generating and storing the secret key and author propose combination of the convolutional neural network with bidirectional associative memory, which is used to recognize the biometric sample, generate the image, and match it with a cryptographic key. The use of this software approach allows today to reduce the probability of errors of the first and second kind in authentication system and absolute number of errors was minimized by an average of 1,5 times. The proportion of correctly recognized images by the comparating together convolutional networks and neural network bidirectional associative memory in the authentication software module increased to 96,97%, which is on average from 1,08 times up to 1,01 times The authors further plan a number of scientific and technical solutions to develop and implement effective methods, tools to meet the requirements, principles and approaches to cybersecurity and cryptosystems for provide integrity and confidentiality of information in experimental computer systems and networks.