I have just started learning cryptography and I am trying to make sense of the direct sum on some binary numbers.
I am trying to find a column of a state space after a Mixcolumns operation has been performed.
For example, to find $c_0$, I have
So i understand exactly what is going on up until the next line:
$=00010011 ⊕ 10011000 ⊕ 10000001 ⊕ 00100001$
How does the direct sum of
$(100001000\oplus100011011)\oplus(110000011\oplus100011011)=00010011 ⊕ 10011000$?
I dont understand how the 9 digit binary numbers direct sum makes an 8 digit binary number??
the next line reads
Again, I do not understand how this answer has been obtained!
Could someone please explain/show how this is done as my notes do not say and I cannot find a method for this online although I am sure I am searching the wrong terms probably.
Help much appreciated. Only a few weeks into learning this! Thanks