Abstract: The rapid advancement of quantum computing necessitates the exploration of alternative mathematical frameworks. This paper introduces a novel hybrid cryptographic protocol that combines tropical semirings with well-established classical primitives. Central to our approach is the Tropical Factorization with Discrete Logarithm Problem (TFDLP), a computationally challenging task that underpins the security of the proposed tropical-based key exchange. The protocol integrates this algebraic method with classical primitives (SHA-256 hashing and AES-GCM encryption) to enhance security, ensuring both quantum resistance and computational efficiency. A detailed security analysis highlights the strengths of our protocol against known cryptanalytic attacks and offers recommendations for secure implementation. Potential use cases for this hybrid scheme include quantum-safe secure messaging, blockchain technologies, and the protection of critical infrastructure systems.

Keywords: Post-quantum Cryptography, Tropical Semiring, Tropical Factorization, Tropical Discrete Logarithm, Hybrid Protocol, AES-GCM Encryption

Pages: 58-68