Problem $4\mathrm{.}5$: For any block cipher, the fact that it is a 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$)$ denote the encryption of a $128-$bit message m under a key k $($the actual bit length of k is irrelevant$).$ Thus,

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 chose the value of the ciphertexts.$)$