Multivariate Post-Quantum Cryptography as an Alternative to Lattice-Based Cryptography

This thesis compares two prominent approaches in post-quantum cryptography – multivariate and lattice-based cryptography – focusing on their theoretical foundations, security properties, and practical applicability. The main objective is to analyze the computational complexity of attacks on selected cryptographic schemes and assess their suitability for real-world deployment. The experimental section provides concrete numerical data illustrating the impact of various parameter configurations on the performance and security of the systems. The results indicate that while lattice-based cryptosystems represent a robust standard for widespread use, multivariate cryptography offers certain advantages, particularly in terms of speed and efficiency, though it demands more careful design of secure parameters. This work contributes to a deeper understanding of the practical aspects of these two cryptographic approaches and offers recommendations for their appropriate implementation in future post-quantum systems.