notes/docs/lectures/cryptography/08_block_cipher_modes.md

Padding Oracle Attacks

Block Cipher Modes

• Most messages don’t come in convenient 128-bit block lengths
• We’ll need to run a block cipher repeatedly on consecutive blocks
• Why not use stream ciphers?
  • Historically, stream ciphers have proven harder to implement

Padding

• ECB and some other modes require message length to be a multiple of the block size

• Public Key Cryptography Standards PKCS7 is a common padding scheme:

  1. Padding bytes are always added to the plaintext before it is encrypted
  2. Each padding byte has a value equal to the total number of padding bytes that are added
  3. The total number of padding bytes is at least one

• 

• Note in this example there are 7 7s and 16 16s

• Note that in the bottom-left example there is 1 1. This could be interpreted as 1 byte of padding or some plaintext. This is why every block must contain at least one padding byte

Electronic Code Book Mode (ECB)

• Just encrypt each block one after another
• This is quick as it can be easily parallelised

Weaknesses

• If x_1 and x_3 are the same, then y_1 and y_3 are also the same.
• ECB allows an attacker to infer information on the plaintext
• Consider a hypothetical bank transfer between two banks that use a fixed key, where the message format is roughly known

• If we start splicing parts of messages together, we can send a legitimate looking message to the bank
• We could also use a chosen plaintext attack by requesting a bank transfer, finding our bank account info and splicing that with another message
• ECB divulges whenever messages or blocks are the same

Here the RGB pixel data of this image has been encrypted using AES in ECB mode

Deterministic vs Probabilistic Encryption

• An encryption scheme is deterministic if some plaintext is mapped to a fixed ciphertext if the key is unchanged
• ECB is deterministic, but most modern modes of operation are probabilistic
• Probabilistic encryption schemes add randomness to the encryption process to achieve a non-deterministic generation of the ciphertext

• r is not a secret

Cipher Block Chaining (CBC)

• XOR the output of each cipher block with the next input
• IV - Initialisation Vector
  • The initial random seed that randomises the whole stream
  • If you encrypted the same plaintext later it will be different
  • An attacker will be unable to tell if y_1 and y_2 are the same message but with different IV or different messages with different IV

y_1 = e_k(x_1 \oplus IV) \\
y_i = e_k(x_i \oplus y_{i-1})

CBC Decryption

• Similar to encryption, but now XOR takes place after decryption
• This is much easier to parallelise

x_1 = d_k(y_1) \oplus IV \\
x_i = d_k(y_i) \oplus y_{i-1}

• If we lost y_1 we would be unable to decrypt y_2
  • We would be able to decrypt y_3 though

Weaknesses

• CBC was the primary method of encryption for many years

  • Now it is less common

• 

• If you flip the first bit in y_2, the same bit is flipped for x_3

  • Changing y_2 means x_2 no longer decrypts properly

Padding Oracles

• Here, an oracle is a system we can query and it will tell us if, once decrypted, some text has valid padding
• A system is unlikely to tell you directly, but it might give away some clue
• Imagine an example api that receives a CBC-encrypted authorisation token

Padding Oracle Attacks

• Let's look at a single decryption block in CBC
• The attack is essentially the same for multiple blocks, just one at a time
  • You attack the last block, which contains the padding

The general strategy is to manipulate bits in the IV to find valid padding and recover z_i

Counter Mode (CTR)

• Encrypt a nonce + counter and use this to mask the plaintext with XOR
  • This is very easily parallelised
  • Each block is encrypted differently, avoiding the issues with ECB mode

• We are now using our block cipher as a stream cipher
  • The keystream generation (AES) is run through blocks
• Decrypting is super easy, just the reverse

Galois Counter Mode

• Extends counter mode to add authenticity
  • The sender definitely sent that message and it hasn’t been modified
• Very similar to counter mode, but adds an authentication tag
  • Uses multiplication in a Galois Finite field GF(2^{128}) modulo x^{128} + x^7 + x^2 + x + 1
• Extremely parallelisable
• Robust to message modification
• Is now standard in TLS1.3