1. Assume 200 people wish to communicate securely using symmetric keys, one symmetric key for each pair of people. How many symmetric keys would this system use in total?
2. What are the subgroups generated by 3, 7, and 10 in the multiplicative group of integers modulo p = 11?
3. Why is a number r a square modulo p, p = 2q + 1 and p and q both prime, if and only if rq = 1 (mod p).