# One-key MAC

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

1. Calculate a temporary value k0 = Ek(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 = Ek(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 ∥ ... ∥ mn−1mn, where m1, ..., mn−1 are complete blocks. (The empty message is treated as one incomplete block.)
2. If mn is a complete block then mn′ = k1mn else mn′ = k2 ⊕ (mn ∥ 10...02).
3. Let c0 = 00...02.
4. For i = 1, ..., n − 1, calculate ci = Ek(ci−1mi).
5. cn = Ek(cn−1mn′)
6. Output t = msb(cn).

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.

## References

1. ^ a b Iwata, Tetsu; Kurosawa, Kaoru (2003-02-24). "OMAC: One-Key CBC MAC". Fast Software Encryption. Lecture Notes in Computer Science. Vol. 2887. Springer, Berlin, Heidelberg. pp. 129–153. doi:10.1007/978-3-540-39887-5_11. ISBN 978-3-540-20449-7.
2. ^ a b c Iwata, Tetsu; Kurosawa, Kaoru (2003). "OMAC: One-Key CBC MAC – Addendum" (PDF). In this note, we propose OMAC1, a new choice of the parameters of OMAC-family (see [4] for the details). Test vectors are also presented. Accordingly, we rename the previous OMAC as OMAC2. (That is to say, test vectors for OMAC2 were already shown in [3].) We use OMAC as a generic name for OMAC1 and OMAC2. `{{cite journal}}`: Cite journal requires `|journal=` (help)
3. ^ Dworkin, Morris (2016). "Recommendation for Block Cipher Modes of Operation: The CMAC Mode for Authentication" (PDF). doi:10.6028/nist.sp.800-38b. `{{cite journal}}`: Cite journal requires `|journal=` (help)
4. ^ Rogaway, Phillip. "CMAC: Non-licensing". Retrieved May 27, 2020. Phillip Rogaway's statement on intellectual property status of CMAC
5. ^ Black, John; Rogaway, Phillip (2000-08-20). Advances in Cryptology – CRYPTO 2000. Springer, Berlin, Heidelberg. pp. 197–215. doi:10.1007/3-540-44598-6_12. ISBN 978-3540445982.
6. ^ Black, J; Rogaway, P. "A Suggestion for Handling Arbitrary-Length Messages with the CBC MAC" (PDF). `{{cite journal}}`: Cite journal requires `|journal=` (help)
7. ^ Iwata, Tetsu; Kurosawa, Kaoru (2003-12-08). "Stronger Security Bounds for OMAC, TMAC, and XCBC". In Johansson, Thomas; Maitra, Subhamoy (eds.). Progress in Cryptology - INDOCRYPT 2003. Lecture Notes in Computer Science. Vol. 2904. Springer Berlin Heidelberg. pp. 402–415. CiteSeerX 10.1.1.13.8229. doi:10.1007/978-3-540-24582-7_30. ISBN 9783540206095.
8. ^ "Impacket is a collection of Python classes for working with network protocols.: SecureAuthCorp/impacket". 15 December 2018 – via GitHub.
9. ^ "Ruby C extension for the AES-CMAC keyed hash function (RFC 4493): louismullie/cmac-rb". 4 May 2016 – via GitHub.