The article presents the results of the analysis of existing problems in key management and digital signature, and also develops and describes the algorithm of the modified Schnorr scheme. It is proposed to create a PGP-like system, proving that the use of a non-positional polynomial number system opens up significant opportunities for increasing the reliability and efficiency of cryptographic procedures in the development of non-traditional algorithms for managing key certificates and digital signatures in cryptographic systems. This system requires a solution that ensures key security at all stages of the key life cycle, minimizes the role of trust, and automates key management. To achieve this, it is important not only to use cryptographic algorithms, but also to effectively manage encryption keys. The theoretical significance is that the reliability of the proposed scheme is shown, and the practical significance is in the possibility of using it to create effective and easily expandable cryptographic systems, showing that the proposed approach can well protect data from possible quantum attacks.