The problems here concern the block cipher introduced $in$ our Module $3$

lecture notes $(assume$ the block size $is$ five bits unless otherwise stated$).$

Suppose the key $isk=15.$

$(a)$ What $is{k}^{-1}?(recall$ that when encrypting $we$ multiply $byk$

modulo $32)$ Enter your answer as an integer.

$(b)$ Encrypt the plaintext

$110110101$

$(note$ that this message requires padding$).$Enter your answer as an binary.

$(c)$ Decrypt the ciphertext

$0100111000$ Enter your answer as an binary

$2$ Given the key $(P,k)=(R{S}_2,25),$ encrypt

$1010001011$ Enter your answer as an binary

$3.$How many keys $of$ the form $(P,k)$ are there? Enter your answer as an integer.

$4.$The block cipher introduced $in$ our Module $3$ lecture notes encrypts

five bits $at$ a time. Now consider the analogous cipher that encrypts

seven bits $at$ a time. Here a key $(w,P,k)$ consists $of$: $(1)$ a bit string $w$

$of$ length $7,(2)$ a permutation $on$ the digits $d_6{d}_5{d}_4{d}_3{d}_2{d}_1{d}_0,$ and $(3)an$

odd integer $k$ modulo $2^7=128.$ How many keys $of$ the form $(w,P,k)$

are there? Enter your answer as an integer.