A blueprint for constructing 3-pass AKE protocols under commitment-based models

The commitment-based AKE model provides a formal security framework for key exchange protocols that avoid long-term cryptographic material, achieving authentication through a final out-of-band verification of session-derived values. Within this model, secure KA-based and KEM-based protocols were previously constructed via a commitment-based MT compiler, yielding optimized 4-pass protocols. In this work, we show that 3-pass protocols secure under this model exist for both primitives. These protocols are constructed ad hoc, following the core ideas of the commitment-based MT authenticator, and their SK security in the unauthenticated model is proved using the same game-based techniques, achieving bounds of the same form as those previously achieved. The resulting protocols provide one-way authentication in three message exchanges.