The numbers ("RAND", SRES, "Kc") form the triplet sent back to the MSC. When a particular IMSI requests access to the GSM core network, the MSC sends the "RAND" part of the triplet to the SIM. The SIM then feeds this number and the "Ki" (which is burned onto the SIM) into the A3 algorithm as appropriate and an SRES is calculated and sent back to the MSC. If this SRES matches with the SRES in the triplet (which it should if it is a valid SIM), then the mobile is allowed to attach and proceed with GSM services.