Generating cryptographic keys, such as passwords or pin codes, involves utilizing specialized algorithms that rely on complex mathematical transformations. These keys necessitate secure storage measures and complex distribution and processing mechanisms, which often incur substantial costs. However, an alternative approach emerges, proposing the generation of cryptographic keys based on the user's biometric data. Since one can generate keys "on the fly," there is no longer a requirement for key storage or distribution. These generated keys, derived from biometric information, can be effectively employed for biometric authentication, offering numerous advantages. Additionally, this alternative approach unlocks new possibilities for constructing information infrastructure. By utilizing biometric keys, the initiation of cryptographic algorithms like encryption and digital signatures becomes more streamlined and less burdensome in storing and processing procedures. This paper explores biometric key generation technologies, focusing on applying deep learning models. In particular, we employ convolutional neural networks to extract significant biometric features from human face images as the foundation for subsequent key generation processes. A comprehensive analysis involves extensive experimentation with various deep-learning models. We achieve remarkable results by optimizing the algorithm's parameters, with the False Reject Rate (FRR) and False Acceptance Rate (FAR) approximately equal and less than 10%. With code-based cryptographic extractors’ post-quantum level of security, we ensure the continued protection and integrity of sensitive information within the cryptographic framework.