1. Client puzzles and amplification Denial-of-service (DoS) attacks attempt to overwhelm a server with a huge volume of requests. Researchers have proposed a defense against DoS attacks called client puzzles: For each request, the server sends the client a freshly generated random challenge r and a difficulty parameter n, and the client has to produce a solution s such that the last n bits of HMAC,(s) are all 0. Clients must present a valid solution to receive service. (a) What is the expected number of HMAC computations for the client to compute the solution? How many HMAC computations does it take for the server to check the solution