Can CRC32(C) ever return to 0?

Question

I'm wondering if CRC32 sum and CRC32C in particular ever return to 0? The simple answer would be "yes" given a large enough data set. However, I was wondering if there is any provisioning in CRC32C standard that would explicitly prevent this from happening.

The use case for this is that I need to be able to check if remote file is empty and all I have is its CRC32C check sum. So, in other words can I infer that if CRC32C is 0 then file is guaranteed to be empty.

If possible, please provide any reference to a standard where this is defined.

Answer 1

@Yanek is almost completely correct.

Just for fun, here is a five-character sequence that gives a CRC-32C of zero: DYB|O. Here is a four-byte sequence in hex that gives zero: ab 9b e0 9b. In fact, that is the only four-byte sequence that can do so. There are no one to three-byte sequences that will give you zero. That is where @Yanek is not exactly right, in that for one, two, or three-byte sequences, zero is not just as likely. The probability of getting a zero is zero in those cases.

Answer 2

A zero is as likely as any other value of a CRC32 checksum. A CRC is essentially the remainder of dividing the entire input (taken as one large binary number) by a pre-selected value. If the input happens to be divisible by that value, the remainder, and thus the CRC, is zero.

Answer 3

How about this, not a 32-bit CRC, though:

1011 | 110011001010.000
       1011
       ----
        1111
        1011
        ----
         1001
         1011
         ----
           1000
           1011
           ----
             1110
             1011
             ----
              1011
              1011
              ----
                  0000 (...)
                  1011
                  ----
                  1011
                  1011
                  ----
                  0000

Or:

1100 | 11001010.000
       1100
       ----
           1010
           1100
           ----
            1100
            1100
            ----
            (...) 0