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.

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 $\backslash$x$04\backslash$x$04\backslash$x$04\backslash$x$04".$

$5$ptsWrite 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.

$15pts$