Re: Hash collision count

Re: Hash collision count

[linux]

*Sigh*.

> A collision -will- occur eventually, and it is trivial to avoid this 
> problem:

Yes, it will occur *eventually*.  Let's put some numbers on this
"eventually" business.

The earth's sun will run out of hydrogen and become a red giant in about
6 billion years, 1.3 * 2^57 seconds.  (Many people say 5 billion. but
I'll round up for safety.)  Suppose we add 1 file per second to our
repository until we are interrupted by the sun's photosphere engulfing
the planet and melting all our computers.

That's a total of n*(n-1)/2 = 1.7 * 2^113 pairs of files which can
possibly collide.  I'll round up to 2^114 for simplicity.

Assuming we have a good uniform hash function, the chance that any given
pair of different file versions produces an identical hash is 1/2^160.

The chance that there are no collsions is (1-1/2^160)^(2^114).  What is
this numerically?  Well, (1-a)*(1-b) = 1 - a - b + a*b.  When multiplying
probabilities very close to 1 (a and b small), the probability is
a little bit larger than (1-(a+b)).

Likewise, when exponentiating proabilities very close to 1, (1-a)^n is
a bit larger than 1-n*a.

Thus, the probability of no collisions is a bit larger than (1 - 2^114/2^160),
or (1 - 2^-46).  The probability of one or more collisions is a bit *less*
than 2^-46, 1 in 70 trillion.


With odds like that, I submit that it's not worth fixing; the odds
of introducing a bug are far higher than that.


If you can't find a hard drive large enough to store 183 quadrillion
file versions, the probability of a collision decreases as the square of
the fraction of that number you do store.  For example, if you only have
400 billion versions, the chance of a collision is around 2^-84.

We have a fair bit of safety margin in our "good uniform hash" assumption.

Running out of 32-bit inode number space is a *far* more urgent problem.

Not to mention that over the next 1000 years of kernel maintainers, one
of them may find something they like better than git.

Hash collision count

[Jeff Garzik]

Ideally a hash + collision-count pair would make the best key, rather 
than just hash alone.

A collision -will- occur eventually, and it is trivial to avoid this 
problem:

	$n = 0
	attempt to store as $hash-$n
	if $hash-$n exists (unlikely)
		$n++
		goto restart
	key = $hash-$n

Tangent-as-the-reason-I-bring-this-up:

One of my long-term projects is an archive service, somewhat like 
Plan9's venti:  a multi-server key-value database, with sha1 hash as the 
key.

However, as the database grows into the terabyte (possibly petabyte) 
range, the likelihood of a collision transitions rapidly from unlikely 
-> possible -> likely.

Since it is -so- simple to guarantee that you avoid collisions, I'm 
hoping git will do so before the key structure is too ingrained.

	Jeff

Re: Hash collision count

[Jeff Garzik]

Jeff Garzik wrote:
> 
> Ideally a hash + collision-count pair would make the best key, rather 
> than just hash alone.
> 
> A collision -will- occur eventually, and it is trivial to avoid this 
> problem:
> 
>     $n = 0
>     attempt to store as $hash-$n
>     if $hash-$n exists (unlikely)
>         $n++
>         goto restart
>     key = $hash-$n


This of course presumes that you know that your new data does not exist 
in the cache.

Otherwise, you would need to hash the on-disk $hash-0 to determine if 
its a collision or a reference.

	Jeff

Re: Hash collision count

[Ray Heasman]

On Sat, 2005-04-23 at 16:27 -0400, Jeff Garzik wrote:
> Ideally a hash + collision-count pair would make the best key, rather 
> than just hash alone.
> 
> A collision -will- occur eventually, and it is trivial to avoid this 
> problem:
> 
> 	$n = 0
> 	attempt to store as $hash-$n
> 	if $hash-$n exists (unlikely)
> 		$n++
> 		goto restart
> 	key = $hash-$n
> 

Great. So what have you done here? Suppose you have 32 bits of counter
for n. Whoopee, you just added 32 bits to your hash, using a two stage
algorithm. So, you have a 192 bit hash assuming you started with the 160
bit SHA. And, one day your 32 bit counter won't be enough. Then what?

> Tangent-as-the-reason-I-bring-this-up:
> 
> One of my long-term projects is an archive service, somewhat like 
> Plan9's venti:  a multi-server key-value database, with sha1 hash as the 
> key.
> 
> However, as the database grows into the terabyte (possibly petabyte) 
> range, the likelihood of a collision transitions rapidly from unlikely 
> -> possible -> likely.
> 
> Since it is -so- simple to guarantee that you avoid collisions, I'm 
> hoping git will do so before the key structure is too ingrained.

You aren't solving anything. You're just putting it off, and doing it in
a way that breaks all the wonderful semantics possible by just assuming
that the hash is unique. All of a sudden we are doing checks of data
that we never did before, and we have to do the check trillions of times
before the CPU time spent pays off.

If you want to use a bigger hash then use a bigger hash, but don't fool
yourself into thinking that isn't what you are doing.

Ciao,
Ray

Re: Hash collision count

[Jeff Garzik]

Ray Heasman wrote:
> On Sat, 2005-04-23 at 16:27 -0400, Jeff Garzik wrote:
> 
>>Ideally a hash + collision-count pair would make the best key, rather 
>>than just hash alone.
>>
>>A collision -will- occur eventually, and it is trivial to avoid this 
>>problem:
>>
>>	$n = 0
>>	attempt to store as $hash-$n
>>	if $hash-$n exists (unlikely)
>>		$n++
>>		goto restart
>>	key = $hash-$n
>>
> 
> 
> Great. So what have you done here? Suppose you have 32 bits of counter
> for n. Whoopee, you just added 32 bits to your hash, using a two stage
> algorithm. So, you have a 192 bit hash assuming you started with the 160
> bit SHA. And, one day your 32 bit counter won't be enough. Then what?

First, there is no 32-bit limit.  git stores keys (aka hashes) as 
strings.  As it should.

Second, in your scenario, it's highly unlikely you would get 4 billion 
sha1 hash collisions, even if you had the disk space to store such a git 
database.


>>Tangent-as-the-reason-I-bring-this-up:
>>
>>One of my long-term projects is an archive service, somewhat like 
>>Plan9's venti:  a multi-server key-value database, with sha1 hash as the 
>>key.
>>
>>However, as the database grows into the terabyte (possibly petabyte) 
>>range, the likelihood of a collision transitions rapidly from unlikely 
>>-> possible -> likely.
>>
>>Since it is -so- simple to guarantee that you avoid collisions, I'm 
>>hoping git will do so before the key structure is too ingrained.
> 
> 
> You aren't solving anything. You're just putting it off, and doing it in
> a way that breaks all the wonderful semantics possible by just assuming
> that the hash is unique. All of a sudden we are doing checks of data
> that we never did before, and we have to do the check trillions of times
> before the CPU time spent pays off.

First, the hash is NOT unique.

Second, you lose data if you pretend it is unique.  I don't like losing 
data.

Third, a data check only occurs in the highly unlikely case that a hash 
already exists -- a collision.  Rather than "trillions of times", more 
like "one in a trillion chance."

	Jeff

Re: Hash collision count

[Petr Baudis]

Dear diary, on Sun, Apr 24, 2005 at 01:20:21AM CEST, I got a letter
where Jeff Garzik <jgarzik@pobox.com> told me that...
> Second, in your scenario, it's highly unlikely you would get 4 billion 
> sha1 hash collisions, even if you had the disk space to store such a git 
> database.

It's highly unlikely you would get a _single_ collision.

> First, the hash is NOT unique.
> 
> Second, you lose data if you pretend it is unique.  I don't like losing 
> data.

*sigh*

We've been through this before, haven't we?

> Third, a data check only occurs in the highly unlikely case that a hash 
> already exists -- a collision.  Rather than "trillions of times", more 
> like "one in a trillion chance."

No, a collision is pretty common thing, actually. It's the main power of
git, actually - when you do read-tree, modify it and do write-tree
(typically when doing commit), everything you didn't modify (99% of
stuff, most likely) is basically a collision - but it's ok since it
just stays the same.

-- 
				Petr "Pasky" Baudis
Stuff: http://pasky.or.cz/
C++: an octopus made by nailing extra legs onto a dog. -- Steve Taylor

Re: Hash collision count

[Jeff Garzik]

Petr Baudis wrote:
> Dear diary, on Sun, Apr 24, 2005 at 01:20:21AM CEST, I got a letter
> where Jeff Garzik <jgarzik@pobox.com> told me that...
> 
>>Second, in your scenario, it's highly unlikely you would get 4 billion 
>>sha1 hash collisions, even if you had the disk space to store such a git 
>>database.
> 
> 
> It's highly unlikely you would get a _single_ collision.

Agreed.


>>First, the hash is NOT unique.
>>
>>Second, you lose data if you pretend it is unique.  I don't like losing 
>>data.
> 
> 
> *sigh*
> 
> We've been through this before, haven't we?

<shrug>

In messing around with archive servers, people get nervous using 
(hash,value) based storage if there isn't even a simple test for collisions.

Someone just told me that one implementation of the Venti archive 
server[1] simply fails the write, if a data item exists with a duplicate 
hash value.  As long as git fails or does something -predictable- in the 
face of the hash collision, I'm satisfied.

	Jeff


[1] http://www.cs.bell-labs.com/sys/doc/venti/venti.html

Re: Hash collision count

[Petr Baudis]

Dear diary, on Sun, Apr 24, 2005 at 02:35:57AM CEST, I got a letter
where Jeff Garzik <jgarzik@pobox.com> told me that...
> Someone just told me that one implementation of the Venti archive 
> server[1] simply fails the write, if a data item exists with a duplicate 
> hash value.  As long as git fails or does something -predictable- in the 
> face of the hash collision, I'm satisfied.

-DCOLLISION_CHECK

See the top of Makefile.

-- 
				Petr "Pasky" Baudis
Stuff: http://pasky.or.cz/
C++: an octopus made by nailing extra legs onto a dog. -- Steve Taylor

Re: Hash collision count

[Jeff Garzik]

Petr Baudis wrote:
> -DCOLLISION_CHECK

Cool.  I am happy, then :)

Make sure that's enabled by default...

Thanks,

	Jeff

Re: Hash collision count

[Imre Simon]

On 4/23/05, Jeff Garzik <jgarzik@pobox.com> wrote:
> Petr Baudis wrote:
> > -DCOLLISION_CHECK
> 
> Cool.  I am happy, then :)
> 
> Make sure that's enabled by default...
> 
> Thanks,
> 
>         Jeff

I would like to second the suggestion that this should be enabled by default.

First, I do think it is highly unlikely that a collision will ever be
found. Actually because of this if one is found it would be an
important byproduct of git and it would probably influence future
system designs. Hence, I believe that it is worth loosing some
efficiency in order to illuminate better this question of the
collision.

I would like to add a reciepe by which one would surely produce a
collision with two files of the same length and quite similar to each
other. I believe that there is a popular belief that this is pretty
much impossible. Of course, we do not have time to execute this
algorithm, but I believe that it convinces everyone that similar files
*do* exist (actually in abundance) with the same hash.

1. Take your favorite text file, at least 160 characters long. 
2. Choose 160 positions in this file.
3. For each position choose your favorite mispelling of that character.
4. Produce all 2^160 text files, all of the same length, choosing for
each position either the original or the alternate character
5. Add an arbitrary file of the same length, different from the above

Two of these files have the same sha1 hash. Or, for that matter, for
any 160 bit  hash the same is true.

Cheers, Imre Simon

Re: Hash collision count

[Tom Lord]

  From: Petr Baudis <pasky@ucw.cz>

  Pasky:

  > No, a collision is pretty common thing, actually. It's the main power of
  > git, actually - when you do read-tree, modify it and do write-tree
  > (typically when doing commit), everything you didn't modify (99% of
  > stuff, most likely) is basically a collision - but it's ok since it
  > just stays the same.

That is not the way people ordinarily use the word "collision".
It's pretty much the opposite of the normal way, actually.

-t

Re: Hash collision count

[Petr Baudis]

Dear diary, on Tue, Apr 26, 2005 at 01:50:31AM CEST, I got a letter
where Tom Lord <lord@emf.net> told me that...
> 
>   From: Petr Baudis <pasky@ucw.cz>
> 
>   Pasky:
> 
>   > No, a collision is pretty common thing, actually. It's the main power of
>   > git, actually - when you do read-tree, modify it and do write-tree
>   > (typically when doing commit), everything you didn't modify (99% of
>   > stuff, most likely) is basically a collision - but it's ok since it
>   > just stays the same.
> 
> That is not the way people ordinarily use the word "collision".
> It's pretty much the opposite of the normal way, actually.

You need to quote me in the context of Jeff Garzik's

> > Third, a data check only occurs in the highly unlikely case that a hash
> > already exists -- a collision.  Rather than "trillions of times", more
> > like "one in a trillion chance."

I just wanted to point out that the data check would hahve to occur
everytime you didn't modify an object.

Kind regards,

-- 
				Petr "Pasky" Baudis
Stuff: http://pasky.or.cz/
C++: an octopus made by nailing extra legs onto a dog. -- Steve Taylor

Re: Hash collision count

[Ray Heasman]

On Sat, 2005-04-23 at 19:20 -0400, Jeff Garzik wrote:
> Ray Heasman wrote:
> > On Sat, 2005-04-23 at 16:27 -0400, Jeff Garzik wrote:
> > 
> >>Ideally a hash + collision-count pair would make the best key, rather 
> >>than just hash alone.
> >>
> >>A collision -will- occur eventually, and it is trivial to avoid this 
> >>problem:
> >>
> >>	$n = 0
> >>	attempt to store as $hash-$n
> >>	if $hash-$n exists (unlikely)
> >>		$n++
> >>		goto restart
> >>	key = $hash-$n
> >>
> > 
> > 
> > Great. So what have you done here? Suppose you have 32 bits of counter
> > for n. Whoopee, you just added 32 bits to your hash, using a two stage
> > algorithm. So, you have a 192 bit hash assuming you started with the 160
> > bit SHA. And, one day your 32 bit counter won't be enough. Then what?
> 
> First, there is no 32-bit limit.  git stores keys (aka hashes) as 
> strings.  As it should.

Oh great, now we have variable length id strings too. And we'll have to
pretend the OS can store infinite length file names.

> Second, in your scenario, it's highly unlikely you would get 4 billion 
> sha1 hash collisions, even if you had the disk space to store such a git 
> database.

Er. So your so-unlikely-the-sun-will-burn-out-first scenario beats my
so-unlikely-the-sun-will-burn-out-first scenario? Why am I not worried?

> > You aren't solving anything. You're just putting it off, and doing it in
> > a way that breaks all the wonderful semantics possible by just assuming
> > that the hash is unique. All of a sudden we are doing checks of data
> > that we never did before, and we have to do the check trillions of times
> > before the CPU time spent pays off.
> 
> First, the hash is NOT unique.

Nooooo. Really?

Why not just use a 8192 bit hash for each 1KiB of data? We could store a
zero length file and store all the data in the filename. Guaranteed, no
hash collisions that way.

We make an assumption that we know is right most of the time, and we use
it because we know our computer will crash from random quantum
fluctuations before we have a chance of bumping into the problem. You do
know that metastability means that every logic gate in your computer
hardware is guaranteed to fail every "x" operations, where x is defined
by process size, voltage and temperature? Sure, any failures in git
would be data dependent rather than random, but that just means we don't
get to store carefully crafted blocks invented by hypothetical
cryptographers that have completely broken SHA.

> Second, you lose data if you pretend it is unique.  I don't like losing 
> data.

You lose data either way. Just we get to burn out a few extra suns
before yours dies, and I can burn out whole galaxies before mine dies by
using a 256 bit hash, anyway.

> Third, a data check only occurs in the highly unlikely case that a hash 
> already exists -- a collision.  Rather than "trillions of times", more 
> like "one in a trillion chance."

Heh. I calculate it has a 50% probability of happening after you have
seen 10^24 input blocks. So, you are off by a factor of a trillion or
so.

Assuming we store 1 KiB blocks with a 160-bit hash, we would be able to
store 1000 Trillion Terabytes before the chance of hitting a collision
goes to 50%. To use marketing units, that is around 10 Trillion
Libraries of Congress. Every 2 bits we add to the hash doubles the
amount of data we can store before we hit a 50% probability of
collision.

I'm not sure how I could convince you that we're arguing about the
number of angels that could dance on a pin.

Ciao,
Ray

Re: Hash collision count

[David Lang]

On Sat, 23 Apr 2005, Jeff Garzik wrote:

> Ideally a hash + collision-count pair would make the best key, rather than 
> just hash alone.
>
> A collision -will- occur eventually, and it is trivial to avoid this problem:
>
> 	$n = 0
> 	attempt to store as $hash-$n
> 	if $hash-$n exists (unlikely)
> 		$n++
> 		goto restart
> 	key = $hash-$n
>
> Tangent-as-the-reason-I-bring-this-up:
>
> One of my long-term projects is an archive service, somewhat like Plan9's 
> venti:  a multi-server key-value database, with sha1 hash as the key.
>
> However, as the database grows into the terabyte (possibly petabyte) range, 
> the likelihood of a collision transitions rapidly from unlikely -> possible 
> -> likely.
>
> Since it is -so- simple to guarantee that you avoid collisions, I'm hoping 
> git will do so before the key structure is too ingrained.

Jeff, this can't work becouse you don't know what objects exist on other 
servers, in fact given the number of different repositories that will 
eventually exist the odds are good that when the colision occures it will 
be when object repositories get combined,

David Lang
-- 
There are two ways of constructing a software design. One way is to make it so simple that there are obviously no deficiencies. And the other way is to make it so complicated that there are no obvious deficiencies.
  -- C.A.R. Hoare