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 HMACr(s) are all 0. Clients must present a valid solution to receive service.

Suppose a unit of work is equivalent to the difficulty of computing one HMAC. If an attacker enjoys an amplification factor of 64 (i.e., the attacker can cause the server to do 64 units of work by expending one unit of work), what should n be to negate this advantage using client puzzles?