$2\mathrm{.}2.$ In each problem, a pair of libraries are described. State whether or not $L_{\text{l}\text{e}\text{f}\text{t}}-=L_{\text{r}\text{i}\text{g}\text{h}\text{t}}.$ If

so$,$ show how they assign identical probabilities to all outcomes. If not, then describe a

successful distinguisher.

Assume that both libraries use the same value of $n.$ Does your answer ever depend on the

choice of $n?$

In part $($a$),\stackrel{}{x}$ denotes the bitwise$-$complement of $x.$ In part $($d$),x$&$y$ denotes the bitwise$-$

AND of the two strings:

$($b$)$

$\backslash$table$[[L_{\text{l}\text{e}\text{f}\text{t}}$