| ## Note | |
| For Problems 2, 4, 5, 6, please provide formal proofs by writing down a reduction like ''Suppose there is a p.p.t. adversary A that does ..., then there is a p.p.t. adversary B that breaks ... as follows: (then describe what B gets, what B generates by itself, and what B sends to A, ...)''. | |
| If you are using the hybrid argument, please define the hybrid distributions clearly. | |
| You may get partial credits by writing down informal proofs or providing proof intuitions. | |
| You can use any theorems except when it is explicitly disallowed in some problems. | |
| For example, in all problems, you can use ''the existence of OWFs implies the existence of PRFs''. | |
| If you want to use Goldreich-Levin's construction of a hardcore bit, you still need to provide the ''construction'' of the hardcore bit, then state the theorem of Goldreich-Levin, but you don't need to prove the theorem of Goldreich-Levin by yourself. |