Air carrier Captain reported possible jamming or interference resulted in GPS failures and reliance on INS; inertial navigation.

Narrative

Arriving over KITOT waypoint headed north toward Cairo; an ADS-B L message appeared on the EICAS. We did the checklist; swapping to the other transponder but no luck. We knew immediately we were being jammed/spoofed as we approached Jordan. The aircraft lost GPS L and GPS R but showed DME-DME and INERTIAL navigation and the aircraft remained on the route without issue. At least an hour past Cairo we expected to see the GPS return to normal but it never did. We contacted dispatch and Maintenance Control to discuss the issue. Maintenance Control couldn't do anything but reset the system after landing. After consulting with dispatch we all agreed we were fine to continue as the aircraft never deviated from the route. Our only concern was Minimum Navigation Performance Specifications over the North Atlantic and again entering Canadian airspace after exiting the random track. As the aircraft approached 30W; the RNP had a value of 7.0 and the aircraft appeared about 1/2 mile off course. Before entering oceanic airspace; we notified both Shanwick and Gander of our spoofing issue. The aircraft corrected itself and was back on course after crossing 30W and we notified Gander of the issue. They assured us we were never in danger of a gross nav error nor were near any aircraft. We continued to EWR without any further issue other than a TERR EICAS; which was expected according to the latest pilot bulletin regarding jamming/spoofing. We landed uneventfully in EWR without any further navigational issues.