CBC-MAC

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 using a secret key k and a block cipher E:

Variable-length messages

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 .

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 authentication

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 in the CBC mode using an IV_{c − 1} and gets the following ciphertext: , where . He also generates the CBC-MAC tag for the IV and the message: 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 (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 also

• 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

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