Hybrid post-quantum Transport Layer Security formal analysis in Maude-NPA and its parallel version

This article presents a security formal analysis of the hybrid post-quantum Transport Layer Security (TLS) protocol, a quantum-resistant version of the TLS protocol proposed by Amazon Web Services as a precaution in dealing with future attacks from quantum computers. In addition to a classical key exchange algorithm, the proposed protocol uses a post-quantum key encapsulation mechanism, which is believed invulnerable under quantum computers, so the protocol's key negotiation is called the hybrid key exchange scheme. One of our assumptions about the intruder's capabilities is that the intruder is able to break the security of the classical key exchange algorithm by utilizing the power of large quantum computers. For the formal analysis, we use Maude-NPA and a parallel version of Maude-NPA (called Par-Maude-NPA) to conduct experiments. The security properties under analysis are (1) the secrecy property of the shared secret key established between two honest principals with the classical key exchange algorithm, (2) a similar secrecy property but with the post-quantum key encapsulation mechanism, and (3) the authentication property. Given the time limit T = 1,722 h (72 days), Par-Maude-NPA found a counterexample of (1) at depth 12 in T, while Maude-NPA did not find it in T. At the same time T, Par-Maude-NPA did not find any counterexamples of (2) and (3) up to depths 12 and 18, respectively, and neither did Maude-NPA. Therefore, the protocol does not enjoy (1), while it enjoys (2) and (3) up to depths 12 and 18, respectively. Subsequently, the secrecy property of the master secret holds for the protocol up to depth 12.