Embodiments described herein are generally directed to methods and devices in which computing devices, and mobile devices in particular, establish a shared encryption key for a device group comprising at least three mobile devices. In accordance with one example embodiment, a public key of a mobile device is computed using a shared password as performed in accordance with authentication acts of a password-authenticated key exchange protocol, and transmitted to at least one other mobile device of the group. A public value is computed as a function of a mobile device private key and of a public key of at least one other mobile device of the device group, in accordance with a group key establishment protocol. The public values of the mobile devices of the device group are used to compute a shared encryption key.