Example Message Modification

For this example, we take the message above (ASCII 'N') and modify the message so it becomes an ASCII y and we still ensure that the ICV remains valid using the process described in Chapter 15.

Stating the problem: Given P(x)= 01001110110, derive P'(x)=01111001XXX where XXX is a valid CRC.

First, the delta between the current message, M(x), and the desired message, N(x), is computed by the exclusive OR of the two values.

M(x) = 01001110
N(x) = 01111001
D(x) = 00110111

Now, the CRC is calculated for the delta value:

          ------------
    1101 |00110111000
             1101
                 1100
                 1101
                   010

The remainder of the division is the CRC of the delta. Now the delta and its CRC are exclusive OR'd with P(x):

P(x)     01001110110
D(x)  00110111000
                    01111001110
CRC(D)                 010
P'(x)  01111001100

Now, P'(x) is shown to be a valid message; the remainder of the CRC calculation is 0.

            ------------
       1101 | 01111001100
              1101
                  1000
              1101
                1011
                1101
                  1101
                  1101
                        0

Because the remainder of the CRC calculation is 0, P'(x) has a valid CRC and the message has been successfully modified.