A user equipment (UE) may be in coverage of a local private non-Third Generation Partnership Project (non-3GPP) wireless network (e.g. a Wi-Fi network) of an enterprise. This non-3GPP wireless network may be part of a private communication system of the enterprise which further includes a local private 3GPP network (e.g. a Long-Term Evolution or “LTE” based network). When the non-3GPP wireless network advertises “single-authentication” support, the UE may complete authentication for non-3GPP access, obtain a Master Session Key (MSK) from the authentication, and generate an Access Security Management Entity (ASME) key (KASME) based on the MSK. In further implementations, the UE may obtain a Globally Unique Temporary Identifier (GUTI) from the non-3GPP wireless network. Subsequently, the UE may perform an attach procedure with the local private 3GPP network without performing an authentication procedure, presenting the GUTI that it obtained from the non-3GPP wireless network for 3GPP access.