We analyze the Extended Access Control (EAC) protocol for authenticated key agreement, recently proposed by the German Federal Office for Information Security (BSI) for the deployment in machine readable travel documents. We show that EAC is secure in the Bellare-Rogaway model under the gap Diffie-Hellman (GDH) problem, and assuming random oracles. Furthermore, we discuss that the protocol achieves some of the properties guaranteed by the extended CK security model of LaMacchia, Lauter and Mityagin (ProvSec 2008). Keywords provable security, authenticated key exchange, German electronic ID card, machine readable travel document.