Problem
You generate a 2048-bit RSA public key (N, e) and corresponding secret key (N, d) via a secure (one-way) RSA generator Krsa. When you register for CSE107, you give the instructor your public key. The instructor will assign you a random 4 (decimal) digit PIN pin that you will use to access your scores through a webpage. Your PIN is sent to you encrypted under your public key. Specifically, the instructor sends you C = (FN (pin))e mod N, where FN : {0, 1, . . . , 9} 4 → ZN* is an injective function with inverse FN-1 such that both FN and FN-1 are computable in less than a millisecond. You can assume the computation of C takes about 100 milliseconds. You decrypt C using (N, d) to recover pin =FN-1 (Cd mod N). The security goal is that it should be impractical for the adversary, given your public key and C, to recover pin.
i. Is the above security goal achieved? Circle either YES or NO below to indicate your answer: YES NO
ii. Justify your answer. The justification for a YES answer should be based on the assumption that Krsa is one-way. The justification for a NO answer should be a practical attack, presented in pseudocode, that, on input (N, e), C, recovers and returns pin, and you should state the running time of the attack.