Highest difficulty that ever was beaten?

[giszmo]

Hi,

again and again and again people ask if the bitocin network could crack sha256 and people reply how we are far from that. The nature of the bitcoin network though is, that we should have a record of how close we ever got. What was the lowest hash ever created by the bitcoin network? Which difficulty would that equal to? Which network speed would it require to run at that difficulty?

I know somebody here has the tools to answer this

[etotheipi]

I posted that calculation a long time ago.  I checked again a month ago, and it was still valid:

https://bitcointalk.org/index.php?topic=29675.0

Summary:  Block 125,552 had a hash that would've been valid at at a difficulty of 36,000,000,000.

However, this has nothing to do with "breaking" sha256, or anything anything of the sort.  It's just luck.  Your statement would be like saying that "one time I rolled 10 dice and they all came up 1, so I must've come close to breaking the dice-rolling game."  SHA256 is no more or less broken because of this.

[giszmo]

I posted that calculation a long time ago.  I checked again a month ago, and it was still valid:

https://bitcointalk.org/index.php?topic=29675.0

Summary:  Block 125,552 had a hash that would've been valid at at a difficulty of 36,000,000,000.

However, this has nothing to do with "breaking" sha256, or anything anything of the sort.  It's just luck.  Your statement would be like saying that "one time I rolled 10 dice and they all came up 1, so I must've come close to breaking the dice-rolling game."  SHA256 is no more or less broken because of this.

cool, thanx for the info. 36,000,000,000 / today's difficulty * today's hash rate would be 274,630TH/s or 275PH/s.

Yes, I know it wouldn't even mean SHA256 was broken if the smallest hash found was actually 0 as shit happens but it might reassure some of those less literate in mathematics that despite the effort of running a several TH/s operation for a serious amount of time, never ever there was a hash found to be smaller than

Code:

00000000000000001e8d6829a8a21adc5d38d0a473b144b6765798e61f98bd1d and not
0000000000000000000000000000000000000000000000000000000000000000

These people should just try to imagine how incredible big this number is and how far we are from 0. If the number were representing our distance to the center of the universe in nanometers, we would still be outside this universe. Far outside.

(If this smallest number found would be 0, it would be an indicator that somebody actually broke the algorithm as one might be lucky but chances this happens by pure luck are just not high enough that the algorithm could be considered save if this ever happens. The one who was lucky might know it was luck but all the cryptographers would assume it wasn't luck. It would be fun though )
 As mentioned above, even if we had touched the 0 once, this would raise concerns ans serious doubts in it being just luck

[kjj]

(If this smallest number found would be 0, it would be an indicator that somebody actually broke the algorithm as one might be lucky but chances this happens by pure luck are just not high enough that the algorithm could be considered save if this ever happens. The one who was lucky might know it was luck but all the cryptographers would assume it wasn't luck. It would be fun though )
 As mentioned above, even if we had touched the 0 once, this would raise concerns ans serious doubts in it being just luck

I would assume it was luck until it happened a second time.  There is nothing special about 0 that makes it less likely than any other hash result.  No one got into a panic when 0000000000000118b413786fcb4f6db133ba1146ab0c33c521d2320f59b18f23 popped up.

[caveden]

again and again and again people ask if the bitocin network could crack sha256

If you see somebody talking about bruteforcing SHA-256, just show him this: https://www.schneier.com/blog/archives/2009/09/the_doghouse_cr.html

One of the consequences of the second law of thermodynamics is that a certain amount of energy is necessary to represent information. To record a single bit by changing the state of a system requires an amount of energy no less than kT, where T is the absolute temperature of the system and k is the Boltzman constant. (Stick with me; the physics lesson is almost over.)

Given that k = 1.38×10^-16 erg/°Kelvin, and that the ambient temperature of the universe is 3.2°Kelvin, an ideal computer running at 3.2°K would consume 4.4×10^-16 ergs every time it set or cleared a bit. To run a computer any colder than the cosmic background radiation would require extra energy to run a heat pump.

Now, the annual energy output of our sun is about 1.21×10⁴¹ ergs. This is enough to power about 2.7×10⁵⁶ single bit changes on our ideal computer; enough state changes to put a 187-bit counter through all its values. If we built a Dyson sphere around the sun and captured all its energy for 32 years, without any loss, we could power a computer to count up to 2¹⁹²

[caveden]

There is nothing special about 0 that makes it less likely than any other hash result. 

But the thing is that any random number you pick will just never happen. (assuming it was really random, and not something you just took from the already existing chain).
That same way, there should never exist a collision in the chain, or anywhere else in the world. The sun will go supernova much before that happens.

[DeathAndTaxes]

again and again and again people ask if the bitocin network could crack sha256

If you see somebody talking about bruteforcing SHA-256, just show him this: https://www.schneier.com/blog/archives/2009/09/the_doghouse_cr.html

I think the summary explains it in a way that even non technical people can grasp the implausibility of brute forcing a 256 private key.

These numbers have nothing to do with the technology of the devices; they are the maximums that thermodynamics will allow. And they strongly imply that brute-force attacks against 256-bit keys will be infeasible until computers are built from something other than matter and occupy something other than space.

"until computers are built from something other than matter and occupy something other than space"
...
"until computers are built from something other than matter and occupy something other than space"
...
"until computers are built from something other than matter and occupy something other than space"

Simply put 256 bit might as well be a quadrillion quadrillion bits from the standpoint of a brute force attack.  This isn't to say SHA-256 can't be defeated.  Like all algorithms it is vulnerable to potential cryptographic flaws.  A hashing algorithm is designed to be one way so the only way to find the input of a particular hash is to try all possible inputs and look for a match.  As discussed above we can conclude that implausible based on all current or even theorized future technology (like a Dyson sphere or capturing the entire output of a Supernova).   A cryptographic flaw breaks that assumption (usually by allowing the attacker to eliminate some possible inputs and thus reduce the search space by many order of magnitudes).  

Is SHA-256 flawed?  Will a flaw be discovered?  Can't prove that it isn't however it is probably one of the most researched algorithms in modern history.   Finding a credible flaw in SHA-256 would elevate a cryptographer to the elites of the field so it certainly isn't for a lack of trying.   

[kjj]

There is nothing special about 0 that makes it less likely than any other hash result. 

But the thing is that any random number you pick will just never happen. (assuming it was really random, and not something you just took from the already existing chain).
That same way, there should never exist a collision in the chain, or anywhere else in the world. The sun will go supernova much before that happens.

The laws of large numbers cuts both ways.

The odds of an honest collision are astronomical, we can safely say that it will "just never happen".  But there are an astronomical number of these unlikely events that will "just never happen".  Some of them will happen just by sheer numbers and dumb luck.  No reason it can't be the one we happen to be watching for and care about.