Let F : $\{0,1\}$k $\backslash$times $\{0,1\}$n $->\{0,1\}$n be a blockcipher. For a string X$,$ let X$[$i$]$ be the i$-$th bit of X$.$ In our convention, string index starts from $1,$ meaning that an n$-$bit string X is X$[1]$X$[2]$ X$[$n$].$

Consider the following implementation of the challenge$-$response protocol. For each n$-$bit challenge N$,$ you are allowed to make as many responses as you like. For each response X$,$ the sever will first compute T $$ FK$($N$),$ where K is the secret key. It then runs the following code:

For i $1$ to n do

If T$[$i$]=$ X$[$i$]$ then output reject and exit

Output accept

Assume that you can measure the running time of the server with reasonable accuracy to know exactly how many iterations the for$-$loop takes. Given a challenge N$,$ recover the secret answer T $$ FK$($N$)$ after O$($n$)$ responses.