$[30$ points$]$ Consider a very simple symmetric block encryption algorithm, in which $32-$bits blocks of

plaintext are encrypted using a $64-$bit key. Encryption is defined as

$C=(Po+K_l)ox{K}_r$

where $C=$ ciphertext; $K=$ secret key; $K_l=$ leftmost $32$ bits of $K$;$K_r=$ rightmost $32$ bits of $K$;$o+=$

bitwise exclusive or; and $ox$ is addition mod$2^{32}.$

Show the decryption equation. That is$,$ show the equation for $P$ as a function of $C,K_l$ and $K_r.$

$[30$ points$]$ A ciphertext has been generated with an affine cipher. The most frequent letter of the

ciphertext is $x,$ and the second most frequent letter of the ciphertext is $Y,$ where $x=$ sum of characters

in your first name modulo $26$ and $Y=$ sum of characters in your last name modulo $26.$ Break this

cipher. If it is not breakable, provide an appropriate justification.

$[40$ points$]$ The one$-$time pad encryption of plaintext mario $($when converted from ASCII to binary in

the standard way$)$ under key $k$ is:

$1000010000000111010101000001110000011101$

What is the one$-$time pad encryption of luigi under the same key? What is the key? $($Show your

work$/$Explain your code$)$