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# AES

## AES-128/192/256

AES offers three different versions:
• AES-128 takes a key of 128 bits (16 bytes)
• AES-192 takes a key of 192 bits (24 bytes)
• AES-256 takes a key of 256 bits (32 bytes)
The term bit security is commonly used to indicate the security of cryptographic algorithms. For example, AES-128 specifies that the best attack we know of would take around
$2^{128}$
operations. This number is gigantic, and it is the security level that most applications aim for.
It is foreseeable that AES-128 will remain secure for a long time.

## AES Interface

Looking at the interface of AES for encryption, we see the following:
• The algorithm takes a variable-length key as discussed previously. For AES-128, this key length is 128 bits.
• It also takes a plaintext of exactly 128 bits.
• The block size is 128 bits.
• It outputs a ciphertext of exactly 128 bits.
Because AES encrypts a fixed-size plaintext, we call it a block cipher. Some other ciphers can encrypt arbitrarily length plaintexts as you will see later in this chapter.
The decryption operation is exactly the reverse of this: it takes the same key, a ciphertext of 128 bits, and returns the original 128-bit plaintext. Effectively, decryption reverts the encryption. This is possible because the encryption and decryption operations are deterministic; they produce the same results no matter how many times you call them.
In technical terms, a block cipher is a keyed permutation: it maps all the possible plaintexts to all the possible ciphertexts. Changing the key changes that mapping.
A permutation is also reversible. From a ciphertext, you have a map back to its corresponding plaintext (otherwise, decryption wouldn't work).
A cipher with a key can be seen as a permutation: it maps all the possible plaintexts to all the possible ciphertexts.
Of course, we do not have the room to list all the possible plaintexts and their associated ciphertexts. That would be
$2^{128}$
mappings for a 128-bit block cipher. Instead, we design constructions like AES, which behave like permutations and are randomized by a key. We say that they are Pseudorandom Permutations (PRPs).

## AES Internals

Let’s dig a bit deeper into the guts of AES to see what's inside. Note that AES sees the state of the plaintext during the encryption process as a 4-by-4 matrix of bytes:
When entering the AES algorithm, a plaintext of 16 bytes gets transformed into a 4-by-4 matrix. This state is then encrypted and finally transformed into a 16-byte ciphertext.
This doesn't really matter in practice, but this is how AES is defined. AES also has a round function that it iterates several times, starting on the original input (the plaintext):
AES iterates a round function over a state in order to encrypt it. The round function takes several arguments including a secret key. (These are missing from the diagram for simplicity.)
Each call to the round function transforms the state further, eventually producing the ciphertext. Each round uses a different round key, which is derived from the main symmetric key during KeyExpansion.
KeyExpansion: From the 128 bit key, 11 separate 128 bit round keys are derived: one to be used in each AddRoundKey step. This step is also known as key schedule.
The combination of the key schedule and the rounds ensure that the slightest change in the bits of the key or the message renders a completely different encryption.
• SubBytes
• Confusion through substitution (using S-Box)
• ShiftRows
• Diffusion through permutation part 1
• MixColumns
• Diffusion through permutation part 2
• AddRoundKey
• Encryption
The first three are easily reversible but the last one is not. It performs XOR(state, round key) thus needs the knowledge of the round key to be reversed:
A typical round of AES. (The first and last rounds omit some operations.) Four different functions transform the state. Each function is reversible as decryption wouldn’t work otherwise. The addition sign inside a circle (⊕) is the symbol for the XOR operation.
• Confusion means that each bit of the ciphertext should depend on several parts of the key, obscuring the connections between the two.
• The property of confusion hides the relationship between the ciphertext and the key.
• This property makes it difficult to find the key from the ciphertext and if a single bit in a key is changed, the calculation of most or all of the bits in the ciphertext will be affected.
• Confusion increases the ambiguity of ciphertext and it is used by both block and stream ciphers.
• In substitution–permutation networks, confusion is provided by substitution boxes (S box).
• Diffusion means that if we change a single bit of the plaintext, then about half of the bits in the ciphertext should change, and similarly, if we change one bit of the ciphertext, then about half of the plaintext bits should change. This is equivalent to the expectation that encryption schemes exhibit an avalanche effect.
• The purpose of diffusion is to hide the statistical relationship between the ciphertext and the plain text. For example, diffusion ensures that any patterns in the plaintext, such as redundant bits, are not apparent in the ciphertext. Block ciphers achieve this by "diffusing" the information about the plaintext's structure across the rows and columns of the cipher.
• In substitution–permutation networks, diffusion is provided by permutation boxes (P box).

## AES-CBC

AES-CBC is bad. AES-CBC is better (but not perfect).
AES-CBC is bad. Since AES encryption is deterministic, and so encrypting the same block of plaintext twice leads to the same ciphertext. This means that by encrypting each block individually, the resulting ciphertext might have repeating patterns:
The famous ECB penguin is an encryption of an image of a penguin using the electronic codebook (ECB) mode of operation. As ECB does not hide repeating patterns, one can guess just by looking at the ciphertext what was originally encrypted. (Image taken from Wikipedia.)
CBC works for any deterministic block cipher (not just AES) by taking an additional value called an initialization vector (IV) to randomize the encryption. Because of this, the IV is the length of the block size (16 bytes for AES) and must be random and unpredictable.
To encrypt with the CBC mode of operation, start by generating a random IV of 16 bytes, then XOR the generated IV with the first 16 bytes of plaintext before encrypting those. This effectively randomizes the encryption. Indeed, if the same plaintext is encrypted twice but with different IVs, the mode of operation renders two different ciphertexts. If there is more plaintext to encrypt, use the previous ciphertext (like we used the IV previously) to XOR it with the next block of plaintext before encrypting it. This randomizes the next block of encryption as well. Remember, the encryption of something is unpredictable and should be as good as the randomness we used to create our real IV:
The CBC mode of operation with AES. To encrypt, we use a random initialization vector (IV) in addition to padded plaintext (split in multiple blocks of 16 bytes).
AES encryption with PyCryptodome:
# AES-CBC encryption
>>> import json
>>> from base64 import b64encode
>>> from Crypto.Cipher import AES
>>> from Crypto.Random import get_random_bytes
>>>
>>> data = b"secret"
>>> key = get_random_bytes(16)
>>> cipher = AES.new(key, AES.MODE_CBC)
>>> iv = b64encode(cipher.iv).decode('utf-8')
>>> ct = b64encode(ct_bytes).decode('utf-8')
>>> result = json.dumps({'iv':iv, 'ciphertext':ct})
>>> print(result)
'{"iv": "bWRHdzkzVDFJbWNBY0EwSmQ1UXFuQT09", "ciphertext": "VDdxQVo3TFFCbXIzcGpYa1lJbFFZQT09"}'
To decrypt with the CBC mode of operation, reverse the operations. As the IV is needed, it must be transmitted in clear text along with the ciphertext. Because the IV is supposed to be random, no information is leaked by observing the value:
The CBC mode of operation with AES. To decrypt, the associated initialization vector (IV) is required.
AES decryption with PyCryptodome:
# AES-CBC decryption
>>> import json
>>> from base64 import b64decode
>>> from Crypto.Cipher import AES
>>>
>>> # We assume that the key was securely shared beforehand
>>> try:
>>> iv = b64decode(b64['iv'])
>>> ct = b64decode(b64['ciphertext'])
>>> cipher = AES.new(key, AES.MODE_CBC, iv)
>>> print("The message was: ", pt)
>>> except (ValueError, KeyError):
>>> print("Incorrect decryption")
An IV needs to be unique (it cannot repeat) as well as unpredictable (it really needs to be random). When an IV repeats or is predictable, the encryption becomes deterministic again, and a number of clever attacks become possible. This was the case with the famous BEAST attack (Browser Exploit Against SSL/TLS) on the TLS protocol.

## AES-CBC-HMAC

So far, we have failed to address one fundamental flaw: the ciphertext as well as the IV in the case of CBC can still be modified by an attacker.
Indeed, there's no integrity mechanism to prevent that! Changes in the ciphertext or IV might have unexpected changes in the decryption. For example, in AES-CBC, an attacker can flip specific bits of plaintext by flipping bits in its IV and ciphertext:
An attacker that intercepts an AES-CBC ciphertext can do the following: (1) Because the IV is public, flipping a bit (from 1 to 0, for example) of the IV also (2) flips a bit of the first block of plaintext. (3) Modifications of bits can happen on the ciphertext blocks as well. (4) Such changes impact the following block of decrypted plaintext. (5) Note that tampering with the ciphertext blocks has the direct effect of scrambling the decryption of that block.
To prevent modifications on the ciphertext, we can use MAC. For AES-CBC, we usually use HMAC in combination with the SHA-256 hash function to provide integrity. We then apply the MAC after padding the plaintext and encrypting it over both the ciphertext and the IV; otherwise, an attacker can still modify the IV without being caught.
The AES-CBC-HMAC construction produces three arguments that are usually concatenated in the following order: the public IV, the ciphertext, and the authentication tag.
Prior to decryption, the tag needs to be verified. The combination of all of these algorithms is referred to as AES-CBC-HMAC and was one of the most widely used authenticated encryption modes until we started to adopt more modern all-in-one constructions.