Abstract
This paper explores the challenges associated with cryptographic key management and highlights the importance of developing efficient protocols to ensure secure and trustworthy key exchange in cryptographic systems. It focuses on the Schnorr digital signature scheme, recognized for its features such as indivisibility, non-repudiation, and resistance to message replay attacks. The study introduces a modified version of the Schnorr scheme, incorporating a non-positional polynomial number system. It outlines the process of generating random numbers for keys and computing necessary values using selected polynomial bases. The implementation of non-positional polynomial number system in the creation of non-traditional digital signature algorithms and key management mechanisms significantly improves both the reliability and performance of cryptographic operations. Furthermore, the paper discusses the potential for adapting the proposed scheme to enhance resistance against quantum computing threats, contributing to the development of quantum-resilient cryptographic solutions.