Modelling and verification of post-quantum key encapsulation mechanisms using Maude

Abstract

Communication and information technologies shape the world’s systems of today, and those systems shape our society. The security of those systems relies on mathematical problems that are hard to solve for classical computers, that is, the available current computers. Recent advances in quantum computing threaten the security of our systems and the communications we use. In order to face this threat, multiple solutions and protocols have been proposed in the Post-Quantum Cryptography project carried on by the National Institute of Standards and Technologies. The presented work focuses on defining a formal framework in Maude for the security analysis of different post-quantum key encapsulation mechanisms under assumptions given under the Dolev-Yao model. Through the use of our framework, we construct a symbolic model to represent the behaviour of each of the participants of the protocol in a network. We then conduct reachability analysis and find a man-in-the-middle attack in each of them and a design vulnerability in Bit Flipping Key Encapsulation. For both cases, we provide some insights on possible solutions. Then, we use the Maude Linear Temporal Logic model checker to extend the analysis of the symbolic system regarding security, liveness and fairness properties. Liveness and fairness properties hold while the security property does not due to the man-in-the-middle attack and the design vulnerability in Bit Flipping Key Encapsulation.