Task $2$: Limits of confidentiality $-$ In this task, you will explore some of the limits of block ciphers in their use within a secure system. Based on the PKCS#$7$ padding and CBC encryption code from Task $1,$ write two "oracle" functions that emulate a web server that wants to use cryptography to protect access to a site administration page. First, at the start of your program generate a random AES key and IV$,$ which will be used in both functions, keeping it constant for the execution of your program $($do not generate a new key or IV for every encryption and decryption$).$ The first function, called submit$(),$ should take an arbitrary string provided by the user, and prepend the string:

userid $=456$; userdata $=$

and append the string:

;session$-$id$=31337$

For example, if the user provides the string

You're the man now, dog $($Use this exact string$)$

submit$()$ would create the string:

userid $=456$; userdata $=$ You're the man now, dog;session$-$id$=31337$

In addition, submit$()$ should: $(1)$ URL encode any $\text{'}$;$\text{'}$ and $\text{'}=\text{'}$ characters that appear in the user provided string; $(2)$ pad the final string $($using PKCS#$7),$ and $(3)$ encrypt the padded string using the AES$-128-$CBC you implemented in Task $1.$ Submit$()$ should return the resulting ciphertext.

The second function, called verify$(),$ should: $(1)$ decrypt the string $($you may use a AES$-$CBC decrypt library or implement your own CBC decrypt$)$; $(2)$ parse the string for the pattern $"$;admin$=$true;" and, $(3)$ return true or false based on whether that string exists. If you've written submit$()$ correctly, it should be impossible for a user to provide input to submit$()$ that will result in verify$()$ returning true.

Now the fun part: use your knowledge of the way CBC mode works to modify the ciphertext returned by submit$()$ to get verify$()$ to return true. Hint: Flipping one bit in ciphertext block $c_i$ will result in a scrambled plaintext block $m_i,$ but will flip the same bit in plaintext block $m_{i+1}.$