If sha-1 were a perfect cyptological hash, the probability of a hash collision 
for a given password would be 1 in 2^160, which, incidentally, is a huge, 
honking, big number.  It isn't however, so the probability is a lttle less.  
Still, using all of the computing resources on earth the many, many millenia 
would take a lot of luck.

There are theoretical attacks on sha-1 that might enable generations of source 
string pairs with a probability of much less than 2^160, but this has nothing 
to do with sha-1 as a password hash.



Jim Starkey


> On Dec 8, 2014, at 7:02 AM, Mark Rotteveel <[email protected]> wrote:
> 
> On Mon, 08 Dec 2014 13:44:36 +0300, Alex Peshkoff <[email protected]>
> wrote:
>> Yes. For password >20 bytes sooner of all exists shorter one with same 
>> hash value.
> 
> But that is technically irrelevant. Although identical hashes are certain
> due to pigeon holing, that doesn't mean shorter passwords (or passwords
> near the hash length) are better than longer passwords. And even then,
> making the assumption that most passwords only use characters between 0x20
> and 0x7E (95 characters out of potentially 256 in a byte) then a very rough
> estimate is that identical hashes might only happen after 50 characters
> (based on 256/95 * 20 = 53.9; a calculation that a cryptologist would
> probably kill me for because it is either totally wrong or too
> conservative).
> 
> Mark
> 
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