Lamport-Diffie + attempting to invert OWF I am studying Lamport-Diffie signature scheme and in my lecture present the follow algorithm  for attempting to invert the one way function $f$, where $f$ is used to compute the public key of this signature from the private key $sk=\left(\begin{array}{rrrrrr} 
x_{1,0} &amp; x_{2,0} &amp; \cdots &amp; x_{l,0} \\
x_{1,1} &amp; x_{2,1} &amp; \cdots &amp; x_{l,1}
\end{array}\right)$. My question is Why will be possible execute the sentence 2, if $x_{i,b}$ are part of private key?
The only requirement is $i,b \neq i^*,b^*$ where $i^*$ is a random value from $1$ to $l$ and $b^* \gets\{0,1\}$ So if $b^*=0$ then $b=1$.

Don't get confused by the $x$, it has nothing to do with the secret key, it's just a variable that later becomes $y_{i,b}=f(x_{i,b})$. It could as well be called $a$.