- Source: 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. The preferred name is now "OMAC2".
The OMAC1 refinement, which became an NIST recommendation in May 2005 under the name CMAC.
OMAC is free for all uses: it is not covered by any patents.
History
The core of the CMAC algorithm is a variation of CBC-MAC 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 that requires less key material (just one key) and named the resulting algorithm One-Key CBC-MAC (OMAC) in their papers. They later submitted the OMAC1 (= CMAC), a refinement of OMAC, and additional security analysis.
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:
Calculate a temporary value k0 = Ek(0).
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.)
If msb(k1) = 0, then k2 = k1 ≪ 1, else k2 = (k1 ≪ 1) ⊕ C.
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:
Divide message into b-bit blocks m = m1 ∥ ... ∥ mn−1 ∥ mn, where m1, ..., mn−1 are complete blocks. (The empty message is treated as one incomplete block.)
If mn is a complete block then mn′ = k1 ⊕ mn else mn′ = k2 ⊕ (mn ∥ 10...02).
Let c0 = 00...02.
For i = 1, ..., n − 1, calculate ci = Ek(ci−1 ⊕ mi).
cn = Ek(cn−1 ⊕ mn′)
Output t = msbℓ(cn).
The verification process is as follows:
Use the above algorithm to generate the tag.
Check that the generated tag is equal to the received tag.
Variants
CMAC-C1 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"
Ruby implementation
References
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)
OMAC Online Test
More information on OMAC
Rust implementation
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