A Linear Secret Sharing Framework for Hybrid Quantum and Post-Quantum Cryptography

Abstract

Quantum resistance is vital for emerging cryptographic systems as quantum technologies continue to advance towards large-scale, fault-tolerant quantum computers. Resistance may be offered by quantum key distribution (QKD), which ideally provides information-theoretic security (ITS) using quantum states of photons, but is limited in practice due to device-dependent loopholes and the reliance on classical channel authentication. An alternative approach uses classical means and is conjectured to be resistant to quantum attacks—so-called post-quantum cryptography (PQC)—but its security relies on the unproven assumption of the hardness of mathematical problems. To address the security and performance challenges present in each, here we introduce a key merging framework to combine QKD and PQC key material based on linear-code secret sharing schemes. In particular, we design joint QKD-PQC key distribution schemes based on Reed-Solomon codes, which achieve high performance while ensuring a high security level. Compared to naive XOR-type schemes, our schemes can achieve a security enhancement of $\Theta (n)$ where $n$ is the number of parallel key distribution links when the key distribution performance is similar. Furthermore, we develop schemes where the attacker needs to break both QKD and PQC links to learn the key bit information. Our hybrid approach paves the way for joint quantum-classical communication networks, which leverage the advantages of both QKD and PQC and can be tailored to the requirements of various practical networks.