Post-quantum Secure Group Messaging

Due to development in quantum computing, we need to create and implement new cryptographic protocols, which are resistant to attacks using a quantum computer, in all practical cases. Last years humans became using messengers to transfer far more important information than earlier, so it is necessary to create new post-quantum secure messaging protocols for peer-to-peer and group communications. In this article, we describe needed security properties, existing ways for the creation of group chats, and our suggestions. We described ways and needed primitives for the creation of a group key establishment scheme based on isogenies of elliptic curves. We describe such protocol as an extended Double Ratchet protocol.