My current textbook (Information Security: Principles and Practice by Mark Stamp) discusses how to determine the CRC of data via long-division, using XOR instead of subtraction to determine the remainder.
If our divisor has N-bits, we append (N-1) 0 bits to the dividend (the data) and then use long-division with XOR to solve for the CRC.
Divisor: 10011 Dividend: 10101011 101010110000 / 10011 = 10110110 R 1010, where 1010 = CRC
I'm able to perform this computation fine. However, the book mentions that in the case of the divisor being 10011, it's easy to find collisions.
I'm missing something here -- why is it easier to find a collision when the divisor is 10011?