Post-Quantum Security of Communication and Messaging Protocols: Achievements, Challenges and New Perspectives

Widely used communication and messaging protocols, e.g., TLS 1.3 and Signal, are insecure against an adversary with a quantum computer. We expect that post-quantum security will become mandatory for a new generation of cryptographic protocols in the nearest 10-15 years. The analysis of existing post-quantum secure cryptographic tools for key exchange, encryption and message authentication based on hard problems in codes, lattices, ring learning with errors and elliptic curve isogenies revealed their advantages and drawbacks. In particular, we conclude, that the main threat to communication and messaging protocols is only pre-quantum security of currently used Diffie-Hellman key exchange protocols. We summarize efficiency and safety results for each class of post-quantum cryptographic schemes and present an experimental implementation of isogeny-based Diffie-Hellman-like key exchange protocol as an illustration of their applicability.