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CBC-MAC

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In cryptography, a Cipher Block Chaining Message Authentication Code, abbreviated CBC-MAC, is a technique for constructing a message authentication code from a block cipher. The message is encrypted with some block cipher algorithm in CBC mode to create a chain of blocks such that each block depends on the proper encryption of the previous block. This interdependence ensures that a change to any of the plaintext bits will cause the final encrypted block to change in a way that cannot be predicted or counteracted without knowing the key to the block cipher.

To calculate the CBC-MAC of message m one encrypts m in CBC mode with zero initialization vector. The following figure sketches the computation of the CBC-MAC of a message comprising blocks m_1\|m_2\|\cdots\|m_x using a secret key k and a block cipher E:

File:CBC-MAC structure (en).svg

Variable-length messagesEdit

Given a secure block cipher, CBC-MAC is secure for fixed-length messages. However, by itself, it is not secure for variable-length messages. An attacker who knows the correct message-tag (i.e. CBC-MAC) pairs (m, t) and (m', t') can generate a third message m'' whose CBC-MAC will also be t'. This is simply done by XORing the first block of m' with t and then concatenating m with this modified m', i.e. by making m'' = m \| [(m_1' \oplus t) \| m_2' \| \dots \| m_x'].


This problem cannot be solved by adding a message-size block (e.g., with Merkle-Damgård strengthening) and thus it is recommended to use a different mode of operation, for example, CMAC to protect integrity of variable-length messages.

Using the same key for encryption and authenticationEdit

One common mistake is to reuse the same key k for CBC encryption and CBC-MAC. Although a reuse of a key for different purposes is a bad practice in general, in this particular case the mistake leads to a spectacular attack. Suppose that one encrypts a message m_0 \| m_1 \| \cdots \| m_{x-1} in the CBC mode using an IV_{c-1} and gets the following ciphertext: c_0 \| c_1 \| \cdots \| c_{x-1}, where c_i = E_k(m_i \oplus c_{i-1}). He also generates the CBC-MAC tag for the IV and the message: t=M(m_{-1} \| \cdots \| m_{x-1}). Now an attacker can change every bit before the last block c_{x-1} and the MAC tag still be valid. The reason is that t = E_k(m_{x-1} \oplus c_{x-2}) = c_{x-1} (this is actually the reason why people make this mistake so often—it allows to increase the performance by a factor of two). Hence as far as the last block is not changed the equivalence t = c_{x-1} holds and thus the CBC-MAC tag is correct.

This example also shows that a CBC-MAC cannot be used as a collision resistant one-way function: given a key it is trivial to create a different message which “hashes” to the same tag.

See alsoEdit

  • CMAC — A block-cipher–based MAC algorithm which is secure for messages of different lengths (recommended by NIST).
  • OMAC and PMAC — Other methods to turn block ciphers into message authentication codes (MACs).
  • One-way compression function - Hash functions can be made from block ciphers. But note, there are significant differences in function and uses for security between MACs (such as CBC-MAC) and hashes.
  • DAA — A (now obsolete) U.S. government standard instantiation of CBC-MAC.

References Edit

  1. ISO/IEC 9797-2:2002
  2. The security of the cipher block chaining message authentication code.


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