A monitoring system monitors authentication sessions both on the air interface between the terminals and the network, and on at least one wired network-side interface between network-side elements of the network. The monitoring system constructs a database of sets of network-side authentication parameters using network-side monitoring. Each set of network-side authentication parameters originates from a respective authentication session and is associated with the International Mobile Station Identity (IMSI) of the terminal involved in the session. In order to start decrypting the traffic of a given terminal, the system obtains the off-air authentication parameters of that terminal using off-air monitoring, and finds an entry in the database that matches the air-interface authentication parameters. From the combination of correlated network-side and off-air authentication parameters, the processor is able to extract the parameters needed for decryption.