Distribution of CRC checksums

Question

I am investigating about the collision propability of CRC checksums when they are used as a hashes. I know how to calculate the collision propability for hash algorithms that are evenly distributed (which means the chance to get all possible checksums for random input data is the same).

What I do not know (and I couldn't find in the web):

1. Are CRC checksums generally [not] evenly distributed?
2. Does the distribution depend from the polynomial?
3. Does the distribution depend from the input data size?

P.S.: I am aware of the restrictions when using CRCs as hashes, so this is not part of this question.

Answer 1

除了恶意意图（您可以通过更改消息中的位来强制执行您喜欢的任何CRC），CRC均匀分布在所有值上。多项式无关紧要，只要它是有效的CRC多项式，并且输入只需要是CRC的大小或更大。