Provably authenticated group key agreement based on braid groups - the dynamic case

Most group key agreement protocols make use of modular exponential operations which require extensive computing resources in devices. Thus, they are unsuitable for resource- constrained devices such as mobile phones, smart cards and intelligent watches. This paper proposes a group key agreement protocol based on braid groups which requires only multiplication operations. The proposed protocol is a scalable one and needs only two rounds for setting a secure group communication. To prevent a man-in-the-middle attack, exchanged messages are simply authenticated by using users' long-term public and private keys instead of signatures. Authentication proofs are also made by using well-known BAN logic. The protocol is designed for dynamic group communication in which member join, member leave, group merge and group partition are discussed. The proposed algorithms take advantage of precomputed values achieved in previous sessions to update keys in subsequent session. This makes the scheme generates fewer communicating messages and lessens user devices' computation. Comparisons of security and complexity among several two-round protocols are also discussed in this article.