Q$5.$ For any block cipher, the fact that it is nonlinear function is crucial to its security. To see this, suppose that we have a linear block cipher EL that encrypts $128-$bit blocks of plaintext into $128-$bit blocks of ciphertext. Let EL $(k,m$ denotes the encryption of a $128-$bit message $m$ under a key $k($the actual bit length of $k$ is irrelevant$),$ thus we have

$EL(k,[m1+m2])=EL(k,m1)+EL($k$,$m$2)$ for all $128-$bit patterns m$1,$ m$2$

means the XOR operator.

Describe how, with $128$ chosen ciphertexts, an adversary can decrypt any ciphertext without knowledge of the secret key k$.($ A "chosen ciphertext" means that an adversary has the ability to choose a ciphertext and then obtain its decryption. Here, you have $128$ plaintext$/$ciphertext pairs to work with and you have the ability to choose the value of the ciphertexts$).$