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Combining two known technologies—biometric and cryptographic—is an urgent problem. The main line of research in this direction is the use of biometric technologies for the control of cryptographic keys. In the present work, a method for the compact representation of fingerprints is proposed, and a method for cryptographic key generation on this basis is developed. The results of the experiments are appropriate for practical application. The generated keys can be used in cryptographic systems with secret and public keys.