One-key MAC

"CMAC" redirects here. For other uses, see CMAC (disambiguation).

One-key MAC (OMAC) is a family of message authentication codes constructed from a block cipher much like the CBC-MAC algorithm. It may be used to provide assurance of the authenticity and, hence, the integrity of data. Two versions are defined:

• The original OMAC of February 2003, which is seldom used.^[1] The preferred name is now "OMAC2".^[2]
• The OMAC1 refinement,^[2] which became an NIST recommendation in May 2005 under the name CMAC.^[3]

OMAC is free for all uses: it is not covered by any patents.^[4]

History

The core of the CMAC algorithm is a variation of CBC-MAC that Black and Rogaway proposed and analyzed under the name "XCBC"^[5] and submitted to NIST.^[6] The XCBC algorithm efficiently addresses the security deficiencies of CBC-MAC, but requires three keys.

Iwata and Kurosawa proposed an improvement of XCBC that requires less key material (just one key) and named the resulting algorithm One-Key CBC-MAC (OMAC) in their papers.^[1] They later submitted the OMAC1 (= CMAC),^[2] a refinement of OMAC, and additional security analysis.^[7]

Algorithm

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 GF(2^b)). Let ≪ denote the standard left-shift operator and ⊕ denote bit-wise exclusive or:

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: 0x1B for 64-bit, 0x87 for 128-bit, and 0x425 for 256-bit blocks.)
3. If msb(k₁) = 0, then k₂ = k₁ ≪ 1, else k₂ = (k₁ ≪ 1) ⊕ C.
4. Return keys (k₁, k₂) for the MAC generation process.

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 one 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 − 1, calculate c_i = E_k(c_i−1 ⊕ m_i).
5. c_n = E_k(c_n−1 ⊕ m_n′)
6. 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.

Variants

CMAC-C1^[8] is a variant of CMAC that provides additional commitment and context-discovery security guarantees.

Implementations

• Python implementation: see the usage of the AES_CMAC() function in "impacket/blob/master/tests/misc/test_crypto.py", and its definition in "impacket/blob/master/impacket/crypto.py"^[9]
• Ruby implementation^[10]