In cryptography

Cryptography

Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

, CMAC (Cipher-based MAC) is a block cipher

Block cipher

In cryptography, a block cipher is a symmetric key cipher operating on fixed-length groups of bits, called blocks, with an unvarying transformation. A block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext...

-based message authentication code

Message authentication code

In cryptography, a message authentication code is a short piece of information used to authenticate a message.A MAC algorithm, sometimes called a keyed hash function, accepts as input a secret key and an arbitrary-length message to be authenticated, and outputs a MAC...

 algorithm. It may be used to provide assurance of the authenticity and, hence, the integrity of binary data. This mode of operation

Block cipher modes of operation

In cryptography, modes of operation is the procedure of enabling the repeated and secure use of a block cipher under a single key.A block cipher by itself allows encryption only of a single data block of the cipher's block length. When targeting a variable-length message, the data must first be...

 fixes security deficiencies of CBC-MAC

CBC-MAC

In cryptography, a cipher block chaining message authentication code , 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...

 (CBC-MAC is secure only for fixed-length messages).

The core of the CMAC algorithm is a variation of CBC-MAC

CBC-MAC

In cryptography, a cipher block chaining message authentication code , 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...

 that Black and Rogaway proposed and analyzed under the name XCBC and submitted to NIST. The XCBC algorithm efficiently addresses the security deficiencies of CBC-MAC, but requires three keys. Iwata and Kurosawa proposed an improvement of XCBC and named the resulting algorithm One-Key CBC-MAC (OMAC

One-key MAC

OMAC is a message authentication code constructed from a block cipher much like the PMAC algorithm.Officially there are two OMAC algorithms which are both essentially the same except for a small tweak....

) in their papers. They later submitted OMAC1, a refinement of OMAC, and additional security analysis. The OMAC algorithm reduces the amount of key material required for XCBC. CMAC is equivalent to OMAC1.

To generate an ℓ-bit CMAC tag (t) of a message (m) using a b-bit block cipher (E) and a secret key (k), one first generates two b-bit sub-keys (k₁ and k₂) using the following algorithm (this is equivalent to multiplication by x and x² in a finite field

Finite field

In abstract algebra, a finite field or Galois field is a field that contains a finite number of elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and coding theory...

 GF(2^b)). Let ≪ signify a standard left-shift operator:

1. Calculate a temporary value k₀ = E_k(0).
2. If msb(k₀) = 0, then k₁ = k₀ ≪ 1, else k₁ = (k₀ ≪ 1) ⊕ C; where C is a certain constant that depends only on b. (Specifically, C is the non-leading coefficients of the lexicographically first irreducible degree-b binary polynomial with the minimal number of ones.)
3. If msb(k₁) = 0, then k₂ = k₁ ≪ 1, else k₂ = (k₁ ≪ 1) ⊕ C.

As a small example, suppose b = 4, C = 0011₂, and k₀ = E_k(0) = 0101₂. Then k₁ = 1010₂ and k₂ = 0100 ⊕ 0011 = 0111₂.

The CMAC tag generation process is as follows:

1. Divide message into b-bit blocks m = m₁ ∥ … ∥ m_n−1 ∥ m_n′ where m₁, …, m_n−1 are complete blocks. (The empty message is treated as 1 incomplete block.)
2. If m_n′ is a complete block then m_n = k₁ ⊕ m_n′ else m_n = k₂ ⊕ (m_n′∥ 10…0₂).
3. Let c₀ = 00…0₂.
4. For i = 1,…, n, calculate c_i = E_k(c_i−1 ⊕ m_i).
5. Output t = msb_ℓ(c_n).

The verification process is as follows:

1. Use the above algorithm to generate the tag.
2. Check that the generated tag is equal to the received tag.

External links

• RFC 4493 The AES-CMAC Algorithm
• RFC 4494 The AES-CMAC-96 Algorithm and Its Use with IPsec
• RFC 4615 The Advanced Encryption Standard-Cipher-based Message Authentication Code-Pseudo-Random Function-128 (AES-CMAC-PRF-128)