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 256-bit blocks of plaintext into...

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 256-bit blocks of plaintext into 256-bit blocks of ciphertext. Let EL(k, m) denote the encryption of a 256-bit message m under a key k (the actual bit length of k is irrelevant). Thus,

Describe how, with 256 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 256 plaintext–ciphertext pairs to work with, and you have the ability to choose the value of the ciphertexts.)