Re: Two questions about USB CRC
- From: riderofgiraffes <mathforum.org_am@xxxxxxxxxxxxxx>
- Date: Mon, 11 Aug 2008 05:28:36 EDT
Let's go back to the first topic.
As you say, the shift register is preloaded with
0s and then encode 00000000 00000000 000000001,
the same answer is got as encoding 00000001.
But even if the shift register is preloaded
with 1s and then encode
00000000 00000000 00000000 00000000 000000001,
the same answer is got as encoding 000000001,
because the period of the CRC5 shift register
(x^5+x^2+1) is 32.
Are you sure? Have you tried it? I've not tried it,
I don't have time just now, but the word "because"
in that sentence I think is not warranted. Every
time you shift out a one you XOR the magic polynomial
code. That does not necessarily mean that after 32
shifts you again end up with all ones.
But regardless, there are only a limited number of
bits in the CRC, and if you allow any input, some
inputs will generate the same CRC. You can only
protect against small changes in inputs of similar
size. For the context of USB this is all you need.
.
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