$1.($Chap$.1,15$ points, $($a$)-5$ points, $($b$)-10$ points$)$

$($a$)$ When Alice encrypts the key $\backslash ($ k $\backslash )$ itself using one$-$time pad, the ciphertext will always be the all$-$zeroes string! So if an eavesdropper sees the all$-$zeroes ciphertext, she learns that Alice encrypted the key itself. Does this contradict Claim $1\mathrm{.}3($p$.16)?$ Why or why not?

$($b$)$ Consider re$-$using plaintexts in OTP $($but with independently random keys for different ciphertexts$)$; if an eavesdropper knows that the same plaintext is encrypted twice $($but doesn't know what the plaintext is$),$ can she learn anything?

Does Claim $1\mathrm{.}3($p$.16)$ have anything to say about a situation where the same plaintext is encrypted more than once?