Air carrier First Officer reported the GPS failed and remained inoperative for the rest of the flight. Maintenance personnel believe it may have been caused by GPS jamming.

Narrative

Approximately 20 NM southwest of DHT flying northwest at FL340 from ZZZ to SLC at XA:30; we received an ATC FAULT EICAS message. We ran the checklist and changed our TCAS from R to L; and the fault returned. We then received a L GPS EICAS message and ran the corresponding checklist. Our GPS further degraded to a GPS EICAS message indicating a failure of both GPS signals. We then had to revert to VOR updates for our Inertial Navigation System (INS); request an alternate arrival that did not require RNAV; request an alternate approach that did not require RNAV; and had to descend into a CFIT risk moderate airfield at high altitude in the mountains at night without any terrain displays or alert capability. We queried Dispatch and ATC about any GPS jamming events that were NOTAM'd for our route; but we were not within the effective range of the only jamming event reported which was in southern Nevada. Our GPS remained degraded and inoperative for the remainder of the flight.Cause: Unknown. The maintenance personnel said they thought it was GPS jamming; but in the aircraft it appeared as a system degradation and failure.Suggestions: Better NOTAM of GPS jamming events and ranges in the domestic network.