Re: Where exactly will arch_fast_hash be used

From: Hannes Frederic Sowa
Date: Mon Dec 08 2014 - 06:25:19 EST


On Sun, Dec 7, 2014, at 22:33, George Spelvin wrote:
> On Sun, 2014-12-07 at 15:06 +0100, Hannes Frederic Sowa wrote:
> > In case of openvswitch it shows a performance improvment. The seed
> > parameter could be used as an initial biasing of the crc32 function, but
> > in case of openvswitch it is only set to 0.
> This is the Fatal Error in thinking that Herbert was warning about.
> The seed parameter doesn't affect CRC32 collisions *at all* if the inputs
> are the same size.
> For fixed-size inputs, a non-zero seed is equivalent to XORing a
> constant into the output of the CRC computation.

Sorry for being unclear, I understood that and didn't bother patching
that '0' with a random seed exactly because of this.

> for *different* sized inputs, a non-zero seed detects zero-padding
> better than a zero one, but *which* non-zero value is also irrelevant;
> all-ones is the traditional choice because it's simplest in hardware.
> A CRC is inherently linear. CRC(a^b) = CRC(a) ^ CRC(b). This makes
> them easy to analyze mathematically and gives them a number of nice
> properties for detecting hardware corruption.
> But that same simplicity makes it *ridiculously* easy to generate
> collisions if you try.

Yes, understood and I totally agree we shouldn't use crc32 hashing in a
lot of places where unsafe data is going to be hashed and inserted into
hash tables.

> One way of looking at a CRC is to say that each bit in the input
> has a CRC. The CRC of a message string is just the XOR of the CRCs
> of the individual bits that are set in the message.
> Now, a CRC polynomial is chosen so that all of the bits of a
> message have different CRCs. Obviously, there's a limit: when the
> message is 2^n bits long, it's not possible for all the bits to
> have different, non-zero n-bit CRCs.
> But a CRC is a really efficient way of assigning different bit patterns
> to different input bits up to that limit.
> (Something like CRC32c is also chosen so that, for messages up to a
> reasonable length, no 3-bit, 4-bit, etc. combinations have CRCs that
> XOR to zero.)
> But, and this might be what Herbert was trying to say and I was
> misunderstanding, if you then *truncate* that CRC, the CRCs of the
> message bits lose that uniqueness guarantee. They're just pseudorandom
> numbers, and a CRC loses its special collision-resistance properties.
> It's just an ordinary random hash, and thanks to the birthday paradox,
> you're likely to find two bits whose CRCs agree in any particular 8 bits
> within roughly sqrt(2*256) or 22 bits.
> Here are a few such collisions for the least significant 8 bits of
> CRC32c:
> Msg1 CRC32c Msg2 CRC32c Match
> 1<<11 3fc5f181 1<<30 bf672381 81
> 1<<12 9d14c3b8 1<<31 dd45aab8 b8
> 1<<5 c79a971f 1<<44 6006181f 1f
> 1<<15 13a29877 1<<45 b2f53777 77
> There's nothing special about the lsbits of the CRC.
> Within 64 bits, the most significant 8 bits have it worse:
> 1<<5 c79a971f 1<<17 c76580d9 c7
> 1<<6 e13b70f7 1<<18 e144fb14 e1
> 1<<19 70a27d8a 1<<38 7022df58 70
> 1<<20 38513ec5 1<<39 38116fac 38
> 1<<13 4e8a61dc 1<<52 4e2dfd53 4e
> 1<<23 a541927e 1<<53 a5e0c5d1 a5
> Now, I'd like to stress that this collision rate is no worse than any
> *other* hash function. A truncated CRC loses its special resistance to
> the birthday paradox (you'd have been much smarter to use 8-bit CRC),
> but it doesn't become especially bad. A truncated SHA-1 will have
> coillisions just as often.
> The concern with a CRC is that, once you've found one collision, you've
> found a huge number of them. Just XOR the bit pattern of your choice
> into both of the colliding messages, and you have a new collision.


> For another example, if you consider the CRC32c of all possible 1-byte
> messages *and then take only the low byte*, there are only 128 possible
> values.
> It turns out that the byte 0x5d has a CRC32c of 0xee0d9600. This ends
> in 00, so if I XOR 0x5d into anything, the low 8 bits of the CRC
> don't change.
> Likewise, the message "23 00" has a CRC32c of 0x00ee0d96. So you can
> XOR 0x23 into the second-last byte of anything, and the high 8 bits of
> the CRC don't change.

A very interesting read, thanks for your mail!

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