The Hash Wall

[pcaston2]

Hello,

While I've seen a lot of consensus that the hash rate is rising and that it's showing no signs of stopping. In fact, it's growing at about 13-18%, barring any giant technological improvements.

My goal is to determine what the 'soft' limit is. That is to say, the limit at which hash rate will remain as a result of people's decisions.

WARNING: I'm going to make a lot of assumptions here, and plug in a lot of values. Feel free to argue any of the assumptions or values, these are merely my interpretation until someone argues a better case. As such, I will try to number my assumptions and values so that they can be easily referred to.

ASSUMPTION #1 - There is a limit:
I believe there is a speed at which the network will remain, once achieved. The limit is dynamic.

ASSUMPTION #2 - People will create the limit:
I am assuming that people will create the limit. This is because the people mining with the most power are doing it for profit. If they are no longer profiting, they will stop mining.
You can argue that people will mine past this point, those people being:

• Those using someone else's power (or 'free' power)
• Those who want simply to support Bitcoin
• Those that don't care or are ignorant of the costs associated with mining

I am assuming that most of the processing power is coming from people intending to make a profit. The people above do not fall into this category because:
The more 'free' power you use, the less likely it is to stay 'free', therefore they are small operations.
Running a miner slowly is just as helpful as mining quickly (except in a rare case where the overall network is terribly slow AND new. In which case it causes security issues), therefore they are small operations. The bigger they are, the more likely they are to have a stake in Bitcoins.
Those that don't care or are ignorant are likely not heavily invested in the Bitcoin system, as they would quickly see a negative profits, therefore they are small operations.
In the event that they are contributing more then a small amount, then the hash rate goes up, and more of the processing power by the profiteers is shut down, thus keeping the hash limit roughly the same, assuming that the processing power is mostly coming from profiteers.

To counter-balance anyone that is mining to or past the limit, a large scale operation has over-head and would likely shut down prior to reaching a balancing point, due to Bitcoin being harder to liquidate then cash. It would just be risk without reward, which is not a good business plan.

Now that we have that out of the way, let's look at...

ASSUMPTION #3 - Variables:
The limit is a function of Bitcoin value, the price of power, and the power consumption per hash. This should be fairly intuitive, the system pays out Bitcoins, which have value, and there is a cost to mining Bitcoins. Metaphoric example:

There is a lottery and in order to partake you need to buy a ticket. As long as the total cost of buying a ticket is lower than the lottery payout, it is in everyone's best interest to play the lottery. A ticket is acquired whenever you perform a hash, and the expense for that ticket is your cost of power, and the lottery value is reflective of the BTC value times the Bitcoins per block.

The understanding is that the payout and the cost to participate are more or less the only factor in determining a (logical) decision on whether or not to play.

Now let's look at some math, and our variables. The easiest thing to agree on is, at present:

There are 25 coins paid out in each block
VARIABLE #1 - Bitcoins per Block (BpB) = 25 BTC/block

While block times might be lower than 10 min right now as the hash rate is ever growing, the rate of growth and the potential to have a negative growth means that it should be very close to one block every 10 minutes.
VARIABLE #2 - Blocks per Hour (BpH) = 60 / 10 = 6 block/hour

The price of Bitcoins is volatile but as it comes into use more frequently, I believe it will stabilize. For now, let's use a value of:
VARIABLE #3 - Bitcoin (BTC) = 130 USD

So now, let's put those 3 together and find out how much USD worth of Bitcoins is generated per hour.

VARIABLE #4 - Mining Rate (MR) = BTC * BpB * BpH = 130 * 25 * 6 = 19,500 USD / h

Okay, so this is more debatable and I might not have good numbers here, or good math, so help me out if you disagree.

ASSUMPTION #4 - No more GPUs:
We can assume GPUs are no longer mining at the limit, as they will be horribly inefficient and extremely slow, thus not contributing very much to the overall processing power of the system. Also with the rise of Litecoins, it will likely always be more profitable to mine something else with a configurable unit.

A Jalapeno (BitForce SC 5GH/s) from Butterfly Labs is supposed to be fairly power efficient, so let's use it for this example.
I will use a shorthand for Gigahash per second (Ghash/s)

5 Ghash/s per 30 Watts (W)
1 Ghash/s per 6 W
0.1667 Ghash/s / W

Therefore, you can arrive at:

VARIABLE #5 - Consumption (m) = 166.66 Ghash/s / kiloWatt hour (kWh)
I'm terrible at electricity but this number seems to correlate directly with the hash/J shown on the hardware comparison page.
https://en.bitcoin.it/wiki/Mining_hardware_comparison#ASIC

So we know how much power it takes to make tickets, how much does that power cost?
The average power cost would contribute to determining where the limit lies. I have no idea on this, so I'm going to use my own power cost.

VARIABLE #6 - Power Cost (p) = 0.10 USD / kWh

PLEASE DEBATE this if you think the average is something else, I have no doubt it is, but someone out there might have a better figure.

Ok, now that we know how much power is, we can determine the cost of a ticket. I'm expressing tickets in Ghash/s. I realize that each hash is a ticket, and that Ghash/s operates over time, but we can ignore time and assume everyone is mining at the same rate. and if for every 1 ticket everyone actually had 10,000 tickets, it makes no difference, so Ghash or hash, it's the same chance.

VARIABLE #7 - Hash Per USD (HpU) = Consumption / Power Cost = m / p = 166.66 / 0.10 = 1666.6 GHash/s /USD

So if it costs 1 USD to make 1666 hashes (over the span of an hour) and the lottery is 19,500 USD

VARIABLE #8 - Limit (L) = Mining Rate * Hash Per USD = mr * HpU = 19500 * 1666.6 = 32498700

So 32,498,700 Ghash/s seems to be the limit, based on those variables.

I'm not sure what the correlation between difficulty and hash speed is, I understand how it works and I know they're related, but I haven't looked into finding the relationship yet.

However, it would appear that the hash rate would grow 284 times greater than the current to reach the threshold.

By calculating the chance of finding a ticket, we can determine what difficulty would yield no profit (it would take more electricity to find a ticket than the payout) this occurs at difficulty between 4,4b and 4.5b, which is 352 times greater than the current.

THEREFORE at the current rate of growth I cannot say that we risk hitting the wall within this bitcoin block speed, using ASIC hardware. I might try to figure out, as the ceiling grows lower by half each 4 years, at what time our speed will hit the approaching wall.

That is not to say that buying ASIC hardware will always be profitable. I may redo this while factoring the average cost of appropriating a miner. Generally as the supply of ASIC increases, the profitability of each unit decreases as well, until it may become impossible if not a lengthy process to make back the initial investment.

**NOTE: All values are assumed for the time of writing, they are (obviously) going to change.

[Ethicoin]

Factor in ASIC's and the fact that ASIC's are going to become 1.) More efficient 2.) Cheaper and 3.) More widespread, due to 1.), 2.) and 3.) the hash rate will keep climbing.

 

[Ethicoin]

Difficulty will keep climbing which means hashrate will keep climbing also 

[Eli0t]

this site has some nice forecasts http://organofcorti.blogspot.ca/2013/05/weekly-network-forecast-27th-may-2013.html

[pcaston2]

The model that I used incorporated an ASIC (Butterfly Lab BitForce SC 5Gh/s) and assumed that if a limit were hit, it would not include any (meaningful) amount of GPUs.

I realize that the efficiency could increase, and this would raise the limit, but that's also handled in the equation (just sub new variables for different efficiency)

While I did work through to try to calculate a limit, the main goal was to establish that at any given time there is one, and it is based on the variables I mentioned.

I would have to guess that the rate at which we improve our efficiency will not be able overcome the halving that will occur roughly every 4 years. Even though the ASIC technology is fairly new, it's based on the architecture that has remained the same in computers for many years, and short of a revolutionary redesign of the computer, I do not foresee breakthroughs in the efficiency of these units.

 I am inclined to agree however, that it may be awhile yet before we approach the limit.

[pcaston2]

Difficulty will keep climbing which means hashrate will keep climbing also 

Difficulty does not climb. Difficulty re-adjusts to adapt to the hashrate. It only increases when the hash rate continually finds blocks earlier than expected.

[Ethicoin]

Difficulty will keep climbing which means hashrate will keep climbing also  

Difficulty does not climb. Difficulty re-adjusts to adapt to the hashrate. It only increases when the hash rate continually finds blocks earlier than expected.

Long term trend is a climbing hash rate. That is why BTC can no longer be profitably mined with a CPU (or even a top of the range tower).

But yes, technically you are correct. Difficulty is fluid and does adjust.

[Ethicoin]

The model that I used incorporated an ASIC (Butterfly Lab BitForce SC 5Gh/s) and assumed that if a limit were hit, it would not include any (meaningful) amount of GPUs.

I realize that the efficiency could increase, and this would raise the limit, but that's also handled in the equation (just sub new variables for different efficiency)

While I did work through to try to calculate a limit, the main goal was to establish that at any given time there is one, and it is based on the variables I mentioned.

I would have to guess that the rate at which we improve our efficiency will not be able overcome the halving that will occur roughly every 4 years. Even though the ASIC technology is fairly new, it's based on the architecture that has remained the same in computers for many years, and short of a revolutionary redesign of the computer, I do not foresee breakthroughs in the efficiency of these units.

 I am inclined to agree however, that it may be awhile yet before we approach the limit.

You've put a lot of thought into this! Myself I believe that ASIC's will ultimately become much more energy efficient (because there is a very high demand for energy efficient ASIC's from consumers and all technologies become more efficient over time - see Ray Kurzweil's law of accelerating returns). If anything I believe quantum computing may be the variable that changes everything ...

Did you factor in an exponential for the energy efficiency? Because the market and demand and the tech indicate that this will most likely be the reality

The first company to make more energy efficient ASIC's will make a lot of money (power costs is the "wall" miners hit when assessing their mining profitability so if someone can make more energy efficient ASIC's this is what ALL the miners on the planet desperately want). Which is why I believe they will do it.

[Ethicoin]

EDIT: updated my above post 

[pcaston2]

That's interesting stuff about the ASICS, I did not know, but it's clear that the power cost is a big factor. Perhaps in places where the power is cheaper, as I believe it is in Iceland (thermal power + polar cooling) would be a good place for an ASIC farm to set up as well.

If quantum computing were to arise, I think that would be the end of Bitcoin. I'm not a quantum computing pro but I believe the idea is that you could compute all possibilities simultaneously, thus you could solve a block instantly. Or just start from block 0 and we-write the entire history if Bitcoin from the very start, saying that you solved each block. Of course then no one would use Bitcoins, so better off to just keep solving blocks instantly.

[DannyHamilton]

That's interesting stuff about the ASICS, I did not know, but it's clear that the power cost is a big factor. Perhaps in places where the power is cheaper, as I believe it is in Iceland (thermal power + polar cooling) would be a good place for an ASIC farm to set up as well.

If quantum computing were to arise, I think that would be the end of Bitcoin. I'm not a quantum computing pro but I believe the idea is that you could compute all possibilities simultaneously, thus you could solve a block instantly. Or just start from block 0 and we-write the entire history if Bitcoin from the very start, saying that you solved each block. Of course then no one would use Bitcoins, so better off to just keep solving blocks instantly.

I thought SHA-256 was quantum computing resistant?  Regardless, even if it isn't, bitcoin would simply switch to a hashing algorithm that is and a checkpoint would be coded into the reference client to prevent anyone fro re-writing the historical blockchain.

[Foxpup]

I'm not a quantum computing pro but I believe the idea is that you could compute all possibilities simultaneously, thus you could solve a block instantly.

By "not a quantum computing pro", I presume you mean "don't know anything about the subject at all and learnt about quantum mechanics from watching Star Trek", right?

I thought SHA-256 was quantum computing resistant?

It is. It is ECDSA that is vulnerable to quantum computers, and which will have to be replaced with a quantum resistant public key algorithm if the need arises (there are already several suitable algorithms, and the only reason we're not using one of them right now is that they haven't been extensively tested and may have unknown flaws).