Please answer the following as completely as possible. Consider a group of 30 people who wish to establish pair-wise secure communications using symmetric-key cryptography.

In other words, each person needs to have a unique shared key with each other person. How many keys need to be exchanged in total?

Suppose c is one block long, a and b are strings that are a multiple of the block length, and M(a||c) = M(b||c).

Here M is CBC-MAC. Then M(a||d) = M(b||d) for any block d. Explain why this claim is true.