AES S-box calculation I am trying to design the s-box for AES. Quoting from Wikipedia, the algorithm for applying affine transformation in AES s-box calculation is

Let s (an 8-bit unsigned variable) be the input number.
Let result be 0.
For 5 times: 
   XOR result with s.
   Rotate s one bit to the left.


My question is why the multiplication is done this way? Why only 5 steps?
This is first half of the calculation presented on the Wiki page.

Notice that every bit of the result is actually a XOR of just five bits:



Now we slightly modify the algorithm you wrote to create five numbers by rotating the original number to the left and only then XOR them together:



As you can see the result is exactly the same.