In GSM, each home network has an AuC database containing user keys Ki. Instead, a process known as key diversification could be used. Key diversification works as follows. Let h be a secure cryptographic hash function and let KM be a master key known only to the AuCs. In GSM, each user has a unique ID known as an IMSI. In this key diversification scheme, a users key Ki would be given by Ki = h(KM, IMSI), and this key would be stored on the mobile. Then given any IMSI, the AuC would compute the key as Ki = h(KM, IMSI).

a. What is the primary advantage of key diversification?

b. What is the primary disadvantage of key diversification?

c. Why do you think the designers of GSM chose not to employ key diversification?