Supposethat $x=(x_{1,\text{d}\text{o}\text{t}\text{s}},x_n)$ and $x^{\text{'}}=(x_1^{\text{'}},$dots,$x_n^{\text{'}})$ aretwosequencesofn plaintext blocks. Let's

suppose $x$ and $x^{\text{'}}$ are encrypted in OFB mode using the same key and the same IV$.$

Show mathematically $($with explanation$)$ how an adversary can compute $xo+x^{\text{'}}.$

Under what conditions in CBC mode can an adversary also potentially compute $x_{i}o+$

$x_j$ utilizing just the ciphertext they see? State this condition and show it

mathematically $($with explanation$).$