Building Group Key Establishment on Group Theory: A Modular Approach

A group key establishment protocol is presented and proven secure in the common reference string mode. The protocol builds on a group-theoretic assumption, and a concrete example can be obtained with a decision Diffie-Hellman assumption. The protocol is derived from a two-party solution by means of a protocol compiler presented by Abdalla et al. at TCC 2007, evidencing the possibility of meaningfully integrating cryptographic and group-theoretic tools in cryptographic protocol design. This compiler uses a standard ring configuration, where all users behave symmetrically, exchanging keys with their left and right neighbor, which are later combined to yield a shared group key.