Enhancing Cryptographic System Security based on Finite Fields

An analysis of modern research in the field of post-quantum cryptography is carried out, which demonstrates the importance of developing algorithms capable of resisting quantum threats. Alternative approaches to optimizing cryptographic systems based on error correction codes have been explored. It is proposed to use $\boldsymbol{G F}(\boldsymbol{q})$ for the development of stable cryptographic systems, which provides a high degree of randomness and unpredictability of encryption. The use of finite Galois fields for key generation enables the adaptation of security levels to specific needs and requirements by selecting the field size, thereby enhancing the security and efficiency of encryption systems.