Compute the output of the MixColumns transformation for the following sequence of input bytes “67 89 AB CD”. Apply the InvMixColumns transformation to the obtained result to verify your calculations. Change the first byte of the input from ‘67’ to ‘77’, perform the MixColumns transformation again for the new input, and determine how many bits have changed in the output.

 You can perform all calculations by hand or write a program supporting these computations. If you choose to write a program, it should be written entirely by you; no use of libraries or public domain source code is allowed in this assignment.