a) Decrypt each of the following cipher texts:

i) Text: "CBBGYAEBBFZCFEPXYAEBB", encrypted with affine cipher with key (7,2).

ii) Text:"KSTYZKESLNZUV", encrypted with Vigenère cipher with key "RESULT".

To decrypt the given cipher texts, we will follow the specific decryption steps for the Affine cipher and the Vigenère cipher.

---

i) Affine Cipher (Key (7, 2))

The Affine cipher encryption function is:

$$
E(x) = (ax + b) \mod 26
$$

Where `a` is the multiplicative key, and `b` is the additive key. The decryption function is:

$$
D(y) = a^{-1}(y - b) \mod 26
$$

To decrypt the message, we need to find the modular inverse of `a` (which is 7 in this case).

1. Find $a^{-1} \mod 26$, where $a = 7$.

   We need to find an integer $x$ such that:

   $$
   7x \equiv 1 \mod 26
   $$

   Using the Extended Euclidean Algorithm, we find that $7^{-1} \equiv 15 \mod 26$.

2. Now, the decryption function becomes:

   $$
   D(y) = 15(y - 2) \mod 26
   $$

3. Applying this to each character in the cipher text "CBBGYAEBBFZCFEPXYAEBB", we first convert each letter into its corresponding number (A=0, B=1, ..., Z=25):

   * C -> 2
   * B -> 1
   * B -> 1
   * G -> 6
   * Y -> 24
   * A -> 0
   * E -> 4
   * B -> 1
   * B -> 1
   * F -> 5
   * Z -> 25
   * C -> 2
   * F -> 5
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