Security analysis and designing unilateral and bilateral two party ideal-lattice based authenticated key establishment protocol for anonymous mobile communication

A two-party authenticated key establishment based on lattices allows two entities to set up a shared secret key securely over a vulnerable transmission medium while ensuring authentication of the participating parties. Given quantum computers promising danger to conventional cryptographic systems, lattice-based protocols utilize quantum-resistant cryptographic primitives (Ring Learning With Error) to provide security guarantees. Many lattice-based authentication key exchange protocols have been designed in the last few years. In this article, the authors have performed a security analysis and they have designed unilateral and bilateral two party ideal-lattice based authenticated key establishment protocols (depending on whether authentication is one-sided (unilateral) or mutual (bilateral), their applications vary) for anonymous mobile communication. In unilateral authentication (HTTPS/TLS 1.3), only one party (typically a server) proves its identity, while the other remains anonymous or does not require explicit authentication. In bilateral authentication (Signal, WhatsApp, Telegram), both parties verify each other’s identities before establishing a secure session. The proposed scheme incorporates forward-secure properties to ensure that even if the long-term key are compromised, the confidentiality of past communication does not hamper. This protocol also provides anonymity, essential for safeguarding individual liberties and preserving confidentiality in sensitive communication scenarios. The protocol possesses a minimum number of exchanged messages and can reduce the number of communication rounds to help minimize the communication overhead.