Air carrier pilot reported GPS jamming and spoofing event that affected the aircraft for a distance after the aircraft had left the area where the event had started.

Narrative

I had taken the first rest for this leg and during my rest; I was told we had experienced GPS jamming/spoofing in the normal/suspected areas near Russia and Iran. Relief crew had then turned off GPS auto updating and ANP stayed around .39-.40 until they were relieved. Few hours later; since we were far enough away from the area of jamming; I selected GPS auto update again to see if possibly that would help lower our ANP back to a normalish number. It had not helped at all. Further into the flight in Kazak airspace; I was out of my seat in the galley and when I returned; the FO had notified me that the LNAV and VNAV experienced a fault and reverted to 'heading hold' and 'alt' and the autopilot had also disengaged. Wasn't a big issue as the FO had re-engaged both LNAV and VNAV and the autopilot. Now; in China airspace; we had received a 5 mile route offset to the right. The plane looked like it was entering the offset normally but then it started deviating off track slightly and then we got another LNAV/VNAV fault and the autopilot disengaged again. We also got an UNABLE RNP caution message. I quickly hit 'heading' and 'alt' and tried to get the plane back on track. ATC had noticed our deviation as well and queried us; we told them we were having navigation problems and are working the issue to which ATC gave us a vector to work the problem. While all this was happening; I had kept our 'pos ref' page up to monitor our RNP/ANP to make sure it wasn't getting any worse. During the deviation event; I had noticed that our ANP got as high as 15.0+ and our RNP was 1.0. It took about a minute for it to slowly come back down to .40 to which we re engaged LNAV and VNAV and proceeded back on course. We also concluded that the GPS auto update should remain inhibited throughout the remainder of the flight and ANP just stayed at .40. Rest of the flight proceeded normally and all systems affected were written up in the logbook. This was one of the worst GPS jamming/spoofing events that I have witnessed. Cause: GPS jamming and spoofing. I did not think that the effects of jamming/spoofing could stay with the flight even though you are well enough away from when it happened but upon reading up on it; it very much is a possibility and that's what seems to have been our situation.