MAC Based on Block Ciphers: DAA and CMAC

 In this section we will firstly study Data Authentication Algorithm (DAA) and then we will move towards Cipher Based Message Authentication (CBMA). 

1. Data Authentication Algorithm (DAA) : 

One of the most widely used MAC is referred to as Data authentication algorithm. 

The algorithm is designed using the cipher block chaining mode of operation of DES as shown in Figure 1. 


Fig. 1: Data Authentication Algorithm

. If necessary, the final block is padded on the right with zeros to make a 64 bit block using the DES encryption algorithm and a secret key, a data authentication code (DAC) is calculated as follows.

O1 = E(k, D1) 

O2 = E(K,[D2 XOR O1]

O3 = E(k, [D3 XOR O2]

:

On = E(K, [Dn XOR On-1]

. The DAC consists of either entire block On or the leftmost M bits of the block with 16<=M<=64.  

Note 1: DAA is applicable on 64 bit message when the message length is greater than 64 bits then it is difficult to use DAA and DAA has less security than upcoming CBMA.


2. Cipher-Based Message Authentication Code (CMAC)  : 

. DAA, which is now considered as obsolete. Then, CMAC, which is designed to overcome the deficiencies of DAA.

. Cipher based message authentication (CMAC) mode of operation uses with AES and triple DES.

.  First, let us define the operation of CMAC when the message is an integer multiple n of the cipher block length b. 

Fig. 2: Message Length is integer multiple of block size

. For AES, b=128, and for triple DES, b = 64
. The message is divided into n blocks (M1, M2, ---, Mn)
. For AES, the key size is 128, 192, or 256 bits, for triple DES the key size is 112 or 168 bits. CMAC is calculated as follows. 

C1 = E(K,M1)

C2 = E(K, [M2 XOR C1])

C3 = E(K, [M3 XOR C2])

:

CN = E(K, [MN XOR CN-1 XOR K1])

T = MSBTlen(CN)

Here T = message authentication code, also referred to as the tag.

Tlen = bit length of T

MSBs(x) = The s leftmost bits of the bit string x. 


Fig. 3: Message Length is not integer multiple of block size

If we use K2 then the two b-bit keys are derived from the K bit encryption as follows: 

L = E(K, 0b)

K1 = L.x

K2 = L.x2 = (Lx).x 

Where multiplication (.) is done in the finite field GF(2b) and x, x2 are first and second order polynomials that are elements of GF(2b). Thus, the binary representation of x2 consist of b-3 zeros followed by 100. The finite field is defined w.r.t an irreducible polynomial that is lexicographically first among all such polynomials with the minimum possible number of nonzero terms.

x6 + x4 + x3 + x + 1

x128 + x7 + x2 + x + 1


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