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Satoshi's Bomb


Why the economic feasibility may lead to the collapse Bitcoin

The author of the article is Alexey Malanov, an expert of Kaspersky Lab's anti-virus technology development department

We will discuss what determines the profitability of mining bitkoy, what principles for adapting the speed of mining were laid in it initially, and why these principles can ultimately lead to the collapse of this crypto currency.

image

We assume that the reader has an idea of ​​the basic mechanisms of Bitcoin operation, such as: blocking , mining , mining pools, reward for the block.

Warning. In this article, we explore the theoretical possibility of developing the described scenario, taking into account the algorithms put into Bitkoyn. We did not set ourselves the goal to analyze in detail the cost structure of the miners, electricity prices in various parts of the world, bank rates and the payback period of equipment.
Attack 51%
In the Bitcoin community, the "Attack of 51%" is well known. If the miner controls more than half of all mining capacities, he has the opportunity:


Pay with their bitkoyanami (for goods, services) or simply exchange them for the usual money.
Start generating blocks that do not include the perfect transaction. Do not show the generated blocks to other miners.
Wait until the goods arrive.
Announce the chain of blocks generated by it.

Wherein:


All other miners will have to accept the version of the blocker of the attacker as the only true one, because it is longer, since the miner has more mining power than all the other players put together;
An attacker gets the goods and keeps his bitkoyny, since in his version of history he did not spend it;
An attacker receives a reward for all the generated blocks, and not for half the blocks he would have generated if he played fairly and built a common chain. Although his income will remain the same until the next recount of complexity;
Most likely in the course of an attack, an attacker will buy another crypto currency for bitcoins, because it is fast, fairly safe and irreversible.

The community agrees that such an attack, if feasible, would cast doubt on the continued operation of the Bitcoin network.

It is also important to understand that for a successful attack it is not necessary to control 51% or more capacities. With some probability it is feasible and with a smaller share. For example, having 30% of the power, the attacker can secretly generate a chain of 5 blocks in a row with a probability of ~ 18%, which will be longer than the public one. In this case, the attacker gets the same advantages as with "Attack 51%." And in case of failure, he can just try again. Most services accepting payments in bitcoins require only five "confirmations", that is, such a generated chain will be enough.
Adaptation of mining complexity
After the generation of every 2016 blocks, the Bitcoin network produces an adaptation of the mining complexity. The norm is considered to be such a complexity, in which one block takes about 10 minutes on average. Thus, the calculation of 2016 blocks should be spent two weeks. If the generation is left, for example, only one week, then after the next recalculation the complexity will be doubled (thus, the next 2016 blocks with the same network power will have to be generated again 2 weeks).

Note that the Bitkoyn network programmatically prohibits changing the complexity of mining more than 4 times for one recalculation.

Direct consequences of these rules. If the mining capacities are added or switched off somewhere in the middle of a period of 2016 blocks, then:


This does not in any way affect the reward that the remaining miners will receive. The reward is determined by the hashtad of the miner, not by its share in the general hashreit. For example, if you turn off half the power, the remaining miners will get twice as many blocks, but for twice as long. The profit will remain.
This directly affects the production rate. If 99% of the miners cease to mine, the next recalculation of the complexity will happen in about 4 years. And the time of generation of one block will be approximately 16 hours.

Bitcombe's authors assumed that the described algorithm would smoothly regulate the power of the network, displacing the least energy efficient equipment and returning the remaining margins to a reasonable extent. However, in reality, such a rare recalculation of complexity leads to another strategy of the miners: they can deceive the algorithm by artificially lowering the performance of the network. After all, when the equipment is suddenly turned off, the profit per day remains at the same level, and with a sudden switch-on, costs are reduced.
Commission for Mining and Free Will of Miners
Miners in addition to the reward for the block (emitted currency) are also taking a commission for carrying out the transactions included in the block. Now the commission is about 10% of the award for the block. We will not dwell on this in detail, but according to our calculations it turns out that the existence of commissions makes the investigated strategy of the miners even more profitable.

Another aspect, the mining pools often do not directly control the mining capacity in its composition. Each participant and equipment owner is free to choose which pool to work in. Usually, the decision to switch from pool to pool is taken from economic considerations.

However, the policy of power on / off, switching of capacities to the mining of the alternative currency (Bitcoin Cash) is determined by the pool manager. In other words, we believe that the described behavior strategy should be accepted and implemented by only ~ 20 participants - owners of pools, the owners of the equipment themselves, though they have "free will", but do not play a role.

Suppose that the total power of all the miners has stabilized, consider one of the strategies for increasing marginality.
An example of the behavior of a miner with stable network power Bitcoin
For simplicity, let's say that you control half the total capacity of the Bitcoin network. You can keep the equipment on all the time and get a reward for about 1008 blocks (50%).

Or you can do the following:

image


Wait until the beginning of the next period of 2016 blocks.
Turn off your power.
To wait, while the remained miners for 4 weeks will win 2016 blocks.
After that, the Bitcoin network will halve the complexity of mining for the next period.
You turn on your power, this will allow the entire network to mumble 2016 blocks in one week.
Only one week you will receive a reward for the same (approximately) 1008 blocks.

Pay attention, in the first scenario for 5 weeks of usual work you would receive a reward for 5/2 * 1008 = 2520 blocks, but would be paid for electricity for all time. In the second scenario, in the same five weeks, you get a reward for 1008 units, but pay for electricity in just one week.

Suppose that the cost of electricity is about 90% of the reward. It is easy to calculate that the profit in the first scenario in five weeks is equivalent to the reward for 2520 * 0.1 = 252 units, and in the second scenario, "reward-costs" = 1008 - 0.9 * 1008/2 = 554.4. That is, the proposed strategy is 2 times more profitable.
Cost-effective behavior of the miner for various parameters
Let:


 The smart miner controls the share of the total network power.
 For all 2016 blocks, the reward in bitkoynah is image.
 For the operation of all network equipment for two weeks, the cost of electricity and maintenance is the sum of image. We assume that the rental of premises and the cost of equipment downtime are negligible. For the sake of simplicity, we intentionally do not take into account the depreciation of the equipment.

Then:


In normal operation, the reward of the miner is image for a period of two weeks.
If the smart miner turns off its equipment, the network will generate 2016 blocks in time in the image larger.
For example, if image, then it takes 1.5 times more time to finish the job.
After the end of the period of adapting the complexity of the network and turning on the equipment of the smart miner, the network will perform the work in image times faster conceived two weeks.
For example, if image, then after switching on its equipment it will take 2/3 of the usual time, about 10 days.
The total duration of the two periods is image;
Thus, in the normal situation (without shutdowns), the miners, working these two periods, earn image
 That is, all the miners receive slightly more than two net profits for such an extended period of time.
A smart miner who works with shutdown will not earn anything in the first period, but in a second, shorter period, he will get image
 That is, an intelligent miner receives one habitual net profit and further saves the share of costs from the cost.
All non-turned miners in the slow period will earn image, and for the fast period  image , because the reward is the same, but they work faster.

It is easy to see that:


If the cost of the miner is exactly equal to his reward (the miner works with zero margin), then the clever approach will allow him to get a net profit of  image .
If the miner works with free electricity (the margin is 100%), then in normal work, he earns more than two profits per period, and when working with idle time - one.
Let's find out how much equipment x should be turned off to maximize the profit of all miners at margin image:

image

image

image

image

image

This is the expression reaches of the maximum at  image . For example, at image smart miners should temporarily turn off 80% of the equipment.
Why do not miners use the described strategy now
image
Increase in the capacity of the Bitkoyn network. For a year the capacity of the network has grown more than 4 times ( Source )
image
Increase in the complexity of Bitcoin network for all time. Since January 2016, complexity has grown 8 times, as well as the cost of bitcoyne ( Source )

The described strategy makes sense only if the overall complexity of the network does not increase. Otherwise, turning off the equipment does not lead to a reduction in complexity and is economically unprofitable.

Until now, the mining capacities have been growing at a high pace; this is a consequence of the growth of bitcoins. The profit of the miner is calculated in bitcoins, and it costs in traditional currency.
image
Bitcoin growth rate ( Source )

However, it is reasonable to assume that if bitkoyn does not endlessly grow in price, sooner or later it will be economically inexpedient to introduce new capacities for mining, and electricity costs will almost equal the reward.
Than threat of turning off powers for mining
When the introduction of new mining capacities ceases, the miners will be able to apply the strategy described above.
image
The distribution of Bitcoin through pools ( Source)

If the mining pools maximize their own profit, then with a margin of 6.25%, you should expect to turn off up to 75% of the capacity. More equipment does not make sense to switch off, because the network will not reduce the complexity more than 4 times.

After that, for an attack of 51%, an attacker needs to either control more than half of the remaining capacity (which is easily achieved with the current capacity distribution) or suddenly include more equipment than worked before (which is not feasible considering the share of the largest pool).

The question arises, but is it advantageous to attack the network to a person who has invested heavily in building up mining capacities? Yes, it is profitable. Given the low margin of mining, the cost of existing equipment for mining is also reduced. In other words, if mining does not bring profit, it is unprofitable to remain honest. In addition, the attacker can remain anonymous, and, among other things, play to lower the price of bitcoins.
Attacking Bitcoin Cash
We deliberately do not consider a situation in which the cost of electricity will quickly and significantly increase, or, more likely, the cost of bitcoins will quickly and significantly decrease. In this case, the strategy of the miners is fairly obvious. With sharp adverse price fluctuations, 100% of the miners will switch off the equipment. On the float will remain, perhaps, those who use free electricity. In this case, the network will simply stop working - for the "two weeks" it will take time commensurate with life, and the impossibility of carrying out transactions will further lower the price of bitcoins.

Just the other day in BitcoinMagazine, our colleague analyzed the situation occurring with currency Bitcoin Cash, which appeared as a result of the split Bitkoyn network on August 1, 2017. In the new currency there is the principle of Emergency Difficulty Adjustment. EDA allows you to adapt the complexity of the Bitcoin Cash network even more often, namely: if less than 6 blocks were formed in 12 hours, the complexity is reduced by 20%. The author comes to conclusions similar to ours, but, what is more important, notes that already now he observes the manipulations of intelligent miners. He fears the destabilization of the Bitcoin Cash network and counts on the rapid intervention of developers.
Conclusion
We analyzed one of the economically viable strategies for the behavior of honest miners in conditions when the capacity of the Bitcoin network will cease to grow. We calculated some key parameters of this strategy and found that following it is beneficial for each participant, but significantly increases the risks of "Attack 51%" and potentially the collapse of the Bitcombe system as a whole.

If all the miners were able to reliably agree, they could go further: turn off all the equipment conditionally except one device. This would be optimal in terms of profit, but fatal in terms of protecting the network.

How should miners act to ensure security? We see here a couple of analogies. The first is the crisis of overproduction, when it happens, producers agree and publicly destroy part of the goods (at least, so it was in the Middle Ages). The second - nuclear disarmament, the countries - the owners of large arsenals - agree on their proportional reduction.

In an ideal world, all miners should agree on disabling some part of their equipment and, most importantly, about its controlled destruction. It is important not only to systematically destroy, but also strictly control its production.

Count on such a "peaceful" result is not necessary. The recent division of the Bitcoin chain into two and the formation of Bitcoin Cash shows that not always the miners can and want to solve common problems together. Perhaps in the future, the ability to cooperate will be a decisive factor.
Time will show how much our theoretical study is in tune with practice.
Papay 19 october 2017, 16:01
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