C-RNTI (Cell Radio Network Temporary Identifier):-
The eNodeB (Evolved Node B) assigns the UE a C-RNTI to identify the UE during exchange of all information over the air. The C-RNTI is assigned during the setup of the RRC Connection (Idle Mode à Connected Mode transition) between a UE and an eNodeB and is valid only for that RRC Connection. Once the UE leaves the coverage area of an eNodeB the RRC Connection must be moved (Inter-eNodeB Handover) and the "new" eNodeB will assign a "new" C-RNTI to the UE. The C-RNTI is an E-UTRAN (Evolved Universal Terrestrial Radio Access Network) specific identifier and the EPC (Evolved Packet Core) Network has no visibility to it.
GUTI (Globally Unique Temporary Identifier):-
The MME (Mobility Management Entity) assigns the UE a GUTI to identify the UE during all message exchanges and procedures with the EPC. The GUTI is assigned during the Attach procedure (Deregistered State à Registered State transition) between the UE and the MME and is valid only as long as the UE is attached to the MME that assigned the GUTI. Once the UE leaves the Tracking Area(s) of an MME the "Attachment" has to be moved (Inter-MME handover) and the "new" MME will assign a "new" GUTI to the UE. Embedded within the GUTI are the PLMN ID of the service provider and the MME Identity. Thus, the GUTI uniquely and globally identifies a UE attached to a specific MME in a specific Service Providers LTE Network in a specific Country. The MME may choose to periodically re-assign a "fresh" GUTI to a UE that is attached to it.
