Post-quantum security of messengers: secure group chats and continuous key distribution protocols

Abstract

Secure group chats in messengers are usually created in two ways: using pairwise channels with continuous key agreement according to the Double Ratchet scheme or using special cryptographic protocols, for example, based on a tree-like scheme for group keys generating. In the first case, each pair of users generates a common key, and the group is formed by the system tools. In the second case, all users of the group collectively generate an iteratively updated shared secret. Both methods have their advantages and disadvantages. If the first method is characterized by high overhead costs for storing and transferring key information, then in the second case, it is not possible to achieve such important security properties for instant messengers as post-compromise security and forward secrecy. However, the post-quantum resistance of these protocols remains unexplored. The article analyzes the existing group chat protocols for classical and post-quantum security. This work identifies the cryptographic primitives and protocol organization methods leading to decreasing cryptographic resistance to attacks using a quantum computer. The article proposes protocols resistant to adversary attacks with a quantum computer and discusses the possibilities of their application. The adversary model and the attack model are expanded and formally described considering attacks using a quantum computer. The main results of the work are secure group messaging protocols secure against attacks using a quantum computer, based on modifications of the tree-like schemes of continuous key agreement. The paper provides the specifications of the developed protocols. Possible technical difficulties in the implementation of post-quantum-resistant group messengers are identified, and directions for further research are outlined.