Widebody; Low Wing; 3 Turbojet Eng
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Distraction; Confusion
ATC Issue All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Environment - Non Weather Related; Human Factors
Getting vectored to ILS 30; controller directed a descent to 2;400 feet (as heard by all three pilots) then quickly followed with a terrain alert climb to 3;000 feet call.  No GPWS alert.  Continued approach without incident.Controller misspoke or didn't realize we were still over high terrain.
On arrival to OAK on radar vectors to the arrival we were at 4;000 feet and the controller told us to descend to 2;400 feet. We read back the clearance and began descending. At 3;000 feet the controller said we were cleared to 3;400 feet and told us to climb to 3;400 feet. We climbed up and continued the approach without incident. All three crew members agreed we had heard 2;400 feet on the original clearance.Incorrect controller assigned altitude.
Air carrier flight crew reported descending to assigned altitude during approach to OAK; but were corrected to climb by NCT TRACON.  ATC issued a low altitude alert.