CBC-MAC on arvau

Wikipedia / CBC-MAC

In cryptography, a cipher block chaining message authentication code (CBC-MAC) is a technique for constructing a message authentication code (MAC) from a block cipher. The message is encrypted with some block cipher algorithm in cipher block chaining (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 , one encrypts in CBC mode with zero initialization vector using a secret key and a block cipher :

CBC-MAC on its own is not secure for variable-length messages (see the discussion below) and is currently used to construct a pseudorandom function family and as a component of the CCM mode.

Use in standards

The CBC-MAC construct is used as part of the CCM mode utilized in IEEE 802.11i and NIST SP 800-97 (as CCMP, the CCM encryption protocol for WPA2), IPsec, and TLS 1.2, as well as Bluetooth Low Energy (as of Bluetooth 4.0, see NIST SP 800-121 Rev2). It is available for TLS 1.3, but not enabled by default in OpenSSL.

CBC-MAC is also used as a "conditioning component" (a.k.a. randomness extractor, a method to generate bitstrings with full entropy) in NIST SP 800-90B.

Standards that define the algorithm

FIPS PUB 113 Computer Data Authentication is a (now obsolete) U.S. government standard that specified the CBC-MAC algorithm using DES as the block cipher.

The CBC-MAC algorithm is also included into ANSI X9.9, ANSI X9.19, ISO 8731-1, and ISO/IEC 9797-1 MAC (Algorithm 1).

Security with fixed and variable-length messages

If the block cipher used is secure (meaning that it is a pseudorandom permutation), then CBC-MAC is secure for fixed-length messages. However, by itself, it is not secure for variable-length messages. Thus, any single key must only be used for messages of a fixed and known length. This is because an attacker who knows the correct authentication tag with and then concatenating , it follows that we compute the MAC for in the usual manner as we will perform an exclusive OR operation with the value derived for the MAC of the first message. The presence of that tag in the new message means it will cancel, leaving no contribution to the MAC from the blocks of plain text in the first message .

This problem cannot be solved by adding a message-size block to the end. There are three main ways of modifying CBC-MAC so that it is secure for variable length messages: 1) Input-length key separation; 2) Length-prepending; 3) Encrypt last block. In such a case, it may also be recommended to use a different mode of operation, for example, CMAC or HMAC to protect the integrity of variable-length messages.

Length prepending

One solution is to include the length of the message in the first block; in fact CBC-MAC has been proven secure as long as no two messages that are prefixes of each other are ever used and prepending the length is a special case of this. This can be problematic if the message length may not be known when processing begins.

Encrypt-last-block

Encrypt-last-block CBC-MAC (ECBC-MAC) is defined as . Compared to the other discussed methods of extending CBC-MAC to variable-length messages, encrypt-last-block has the advantage of not needing to know the length of the message until the end of the computation.

Attack methods against incorrect use

As with many cryptographic schemes, naïve use of ciphers and other protocols may lead to attacks being possible, reducing the effectiveness of the cryptographic protection (or even rendering it useless). We present attacks which are possible due to using the CBC-MAC incorrectly.

Using the same key for encryption and authentication

One common mistake is to reuse the same key 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:

, remains the same. We assume, for the purposes of this example and without loss of generality, that the initialization vector used for the encryption process is a vector of zeroes.

Bob first decrypts the message received using the shared secret key .

, is given by:

Notice that this expression is equal to

, was produced, but the tag for this message matched the tag of the original, and Bob was unaware that the contents had been modified in transit. By definition, a Message Authentication Code is broken) which produces the same tag as the previous message, . It follows that the message authentication protocol, in this usage scenario, has been broken, and Bob has been deceived into believing Alice sent him a message which she did not produce.

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.

Allowing the initialization vector to vary in value

When encrypting data using a block cipher in cipher block chaining (or another) mode, it is common to introduce an initialization vector to the first stage of the encryption process. It is typically required that this vector be chosen randomly (a nonce) and that it is not repeated for any given secret key under which the block cipher operates. This provides semantic security, by means of ensuring the same plain text is not encrypted to the same cipher text, allowing an attacker to infer a relationship exists.

When computing a message authentication code, such as by CBC-MAC, the use of an initialization vector is a possible attack vector.

). The result of this operation is the input to the block cipher for encryption.

However, when performing encryption and decryption, we are required to send the initialization vector in plain text - typically as the block immediately preceding the first block of cipher text - such that the first block of plain text can be decrypted and recovered successfully. If computing a MAC, we will also need to transmit the initialization vector to the other party in plain text so that they can verify the tag on the message matches the value they have computed.

If we allow the initialization vector to be selected arbitrarily, it follows that the first block of plain text can potentially be modified (transmitting a different message) while producing the same message tag.

. If no further changes are made to the plain text, the same tag will be derived despite a different message being transmitted.

If the freedom to select an initialization vector is removed and all implementations of CBC-MAC fix themselves on a particular initialization vector (often the vector of zeroes, but in theory, it could be anything provided all implementations agree), this attack cannot proceed.

To sum up, if the attacker is able to set the IV that will be used for MAC verification, he can perform arbitrary modification of the first data block without invalidating the MAC.

Using predictable initialization vector

The simplest countermeasure is to encrypt the IV before using it (i.e., prepending IV to the data). Alternatively MAC in CFB mode can be used, because in CFB mode the IV is encrypted before it is XORed with the data.

Another solution (in case protection against message replay attacks is not required) is to always use a zero vector IV. are the same message, by definition they will have the same tag. This is not a forgery, rather the intended use of CBC-MAC.