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 EnLinear that encrypts

$2$

$5$

$6$

$-$

bit blocks of plaintext into

$2$

$5$

$6$

$-$

bit blocks of ciphertext. Let EnLinear

$($

$$

$,$

$$

$)$

$$denote the encryption of a

$2$

$5$

$6$

$-$

bit message

$$

under a key

$$

$($

the actual bit length of

$$

$$is irrelevant

$)$

$.$

$$Thus$,$

EnLinear

$($

$$

$,$

$[$

$$

$1$

$$

$+$

$$

$2$

$]$

$)$

$=$

EnLinear

$($

$$

$,$

$$

$1$

$)$

$$

$+$

EnLinear

$($

$$

$,$

$$

$2$

$)$

$$for all

$1$

$2$

$8$

$-$

bit patterns

$$

$1$

$,$

$$

$2$

$.$

Describe how, with

$2$

$5$

$6$

$$chosen ciphertexts, an adversary can decrypt any ciphertext without

knowledge of the secret key

$$

$.$

$($

A "chosen ciphertext" means that an adversary has the ability to

choose a ciphertext and then obtain its decryption. Here, you have

$2$

$5$

$6$

$$plaintext

$/$

ciphertext pairs

to work with, and you have the ability to choose the value of the ciphertexts.

$)$