The looming threat of quantum computing necessitates the development of cryptographic protocols that resist quantum attacks. While most post-quantum research has focused on lattice-based and code-based systems, semiring-based cryptography—particularly over tropical algebra—offers a novel, lightweight, and potentially efficient alternative. This work proposes a hybrid cryptographic framework that integrates semiring-based key exchange with established quantum-resilient methods, including hash-based cryptography as outlined in NIST’s Post-Quantum Cryptography Project, to ensure forward secrecy. We further explore the potential of embedding our semiring-based scheme into blockchain architectures, targeting applications in decentralized identity, post-quantum key management, and secure wallet communication. The proposed framework facilitates key exchange through tropical matrix semirings and converts the resulting shared key into a secure AES key via cryptographic hashing. Our findings suggest that semiring-based cryptography can be both a stand-alone post-quantum solution and a complementary building block in hybrid systems. We discuss the security assumptions, performance metrics, and integration scenarios for blockchain environments, and highlight the potential of semiring structures to contribute to the design of quantum-resilient distributed ledgers. Our findings indicate that semiring-based cryptography, when appropriately designed, could serve as a valuable component of the future post-quantum cryptographic ecosystem, offering both theoretical novelty and practical potential.