CRC32C magic value -> shouldn't it be 0

[Luben Tuikov <ltuikov@yahoo.com>]

Hello there,

I've been implementing CRC32C for several days now and I was NEVER
able to get the results of the test cases of iSCSI draft v8.

I got to a point where I worked out the math myself and the results I
get are consistent.

I have two implementations, one simple shifting and another with table
lookup. They both yield the same results.

The problem is that any legal transformations, reorderings, etc, as
specified by the link, TCP, Ethernet, etc. protocols are transparent to
the sender and the receiver. E.g. data sent is the same data received
(assuming there was no noise or data corruption -- i.e. illegal
transformations).

If this is observed then I get ``magic'' value of 0 rather than
0x1c2d19ed. Here is my reasoning:

In the context of pp. 150-151 of iSCSI draft v8:

M(x) has been built MSB(lsb), i.e. the coefficient to x^(n-1), a_(n-1)
is the LS bit of the MS Byte, ... so on to a_0 which is the MS bit of
the LS byte.

Let M'(x) = x^32*M(x).

Then R(x) is computed as usual and then R(x) = ~R(x) as per the draft,
i.e. complement the coefficeints to yield r_31, ..., r_0, which are
appended in that order to the message. Call this message M''(x).

Now M''(x) looks like this:
  M''(x) = a_(n+31)*x^(n+31) + ... + r_31*x^31 + ... + r_0.

Now, this M''(x) is sent verbatim, and then received verbatim on the
other end of the wire -- as mentioned above -- assuming there was no
noise (all other link, Ethernet, etc. transformations are transparent
to us).

Now that the message has been received:
Then R(x) is computed as usual and then R(x) = ~R(x) (note the
algorithm symmetricity). At this point I get 0 and not 0x1c2d19ed. The
reason being is that M''(x) has a remainder ~0, since the remainder was
complemented before attaching it to M'(x) to form M''(x). But since we
always complement, we get R(x) = ~~R(x) (once before sending and once
after receiving) so the remainder is 0 as it should be.

Any comments, pointers, etc. would be greatly appreciated.

-l



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