Exercise $3$: PKCS#$7$ padding $[20$ pts$]$

The PKCS#$7$ padding scheme is commonly used to pad irregularly$-$sized plaintext messages to a specific block length before encryption, and is described in RFC$5652.$ The algorithm simply consists in appending the required number of bytes up to nearest multiple of the block length. The value of each appended byte is equal to the number of bytes added. The maximum length of the pad is therefore $255.$ If the plaintext size is already a multiple of the block length, padding is still required. In this case, an entire block of padding bytes will be used. To remove the padding after decryption, the last byte of the decrypted ciphertext is read, which indicates how many bytes $($of the same value$)$ should be stripped from the end.

For this exercise, do NOT use any library$/$package in your code.

$1.$ Write a function pkcs$($plaintext$,$ length$)$ in Python that takes a plaintext $($plaintext$)$ and a desired block length $($length$)$ as input and applies the PKCS#$7$ padding scheme. The function should return the padded input. An exception should be thrown if the block length is greater than the maximum pad length, using: raise Exception $("$Invalid block size"$)$

For instance, for the message "YELLOW SUBMARINE" and a block size of $20,$ the output should be

"YELLOW SUBMARINE$)\backslash$times $04\backslash \backslash$times $04\backslash \backslash$times $04\backslash \backslash$times $04".$

$2.$ Write a function validate pkcs$($plaintext$,$ length$)$ in Python that verifies the validity of the padding, and returns an unpadded string. The function should throw exceptions using raise Exception$("$Invalid padding"$)$ when: $1)$ the length of the plaintext indicates that no padding has been used; $2)$ the value for the pad length is incompatible with the block length; $3)$ the value of the padding bytes is incorrect. $[15$ pts$]$

Prepare a single Python file named exercise$3.$py that contains both functions.

Make sure to use the exact exception messages given above throughout this exercise; otherwise, your function will not be evaluated properly for assessment.