Computer Science // Cryptology

Please Expain and label each answer

3. Suppose we use symmetric keys for authentication and each of N users must be able to authenticate any of the other N 1 users. Evidently, such a system requires one symmetric key for each pair of users, or on the order of N2 keys. On the other hand, if we use public keys, only N key pairs are required, but we must then deal with PKI issues.

a. Kerberos authentication uses symmetric keys, yet only N keys are required for N users. How is this accomplished?

b. In Kerberos, no PKI is required. But, in security, there is no free lunch, so what's the tradeoff?