スケーリングビットコイン・ワークショップ: Montreal 2015

Security of diminishing block subsidy

Miles Carlsten

Harry Kalodner

Arvind Narayanan

Miners no longer incentivized to mine all the time. The future of mining hardware. Impact on the bitcoin ecosystem. Implications and assumptions of the model.

Are minting rewards and transaction fees the same? Transaction fees are time-dependent. A miner can only claim transaction fees as transactions are added to their block. As transaction fees start to dominate the block reward, they become time-dependent. We are modeling this block reward as a linear function of time, we have this factor B which might be initial minting reward, and we have some scaling factor, the block reward is like "b + at". Something that can be added to this plot is that miners have a set expense to mine, and if miners are not going to recoup their costs, it's not worth them to mine that block.

Above that threshold of worth their time to mine the block, and below it is not worth the time to mine the block. You could see this happening over multiple blocks. There are periods where it's worth the miner's time to mine, and periods where it's not. I am going to refer to these times as where it's not worth their time to mine, as the "mining gaps".

Okay but first the future of mining hardware. It's becoming more commoditized. The efficiency of mining hardware is not changing much. And it's becoming cheaper. Moore's law is not in effect. The cheaper, longer-lasting mining hardware will be more available to everyone. This will have some effects with regards to block size. We've taken data from the bitcoin wiki hardware comparison page. You see the five most efficient machines cited on the page, and the five most efficient machines and it says this on the page, they fudged their numbers a bit to take advantage of miners. It's very much a step function. It makes sense. The mining hardware initially at GPUs, then FPGAs and then ASICs. What's interesting about this plot is that if you look at a single generation of hardware, the efficiency hasn't changed much. This shows that over the last 18 months, there hasn't been much of an efficiency change in mining ASICs hardware. The price of ASICs have actually been going down when you measure it in the dollar cost of the machine per gigahash of hashrate. Efficiency isn't changing, mining hardware isn't being made obsolete, it's not that it's not going to be effective; and it is going to be reasonable for more people to acquire hash power because the cost of hash power is going down.

Can we attach numbers to these gaps? It starts with how the gap is calculated. All miners will make a decision about when to start mining. They will be making this decision on an instantaneous basis. Whether the cost of electricity of computing a hash is less than the expected reward for each hash that they compute. We have created a mathematical framework that describes when it's optimal for miners to start mining. As a proof of concept, we showed a proof of concept simulation for when it's ideal for miners to start mining. We tried to model the bitcoin network accurately, we change the block reward and we also increase the amount of profit from transaction fees. Using these parameters, we predict an ideal gap of about 177 second.

In this simulation, we have miners mining at this ideal gap. If any miner tries to mine earlier or later, their profits actually go down. So what does this mean for the future? Can we predict when the gap is going to occur or when the time is going to happen? If we make the economic argument that miners take their profits and invest hardware, we can model the behavior of the gap in the future. In this simulation, we have time on the x axis and we have the predicted ideal gap on the y-axis and the kind of ... we have the x axis labeled here, we are at block 370k. What this predicts, and oh this uses the same model as the bitcoin system, trying to keep it realistic. We have the actual block minting reward and we make the assumption that as the block oreward, or as the minting reward is diminished, what was .. will be rolled into the transaction fees. The exact description is not .. we see similar effects regardless.

What you see in this plot is that at the next block halving, it will be ideal for miners to mine at the gap. The ideal gap will increase as miners invest in better hardware. I was talking about the commoditization of hardware earlier. This curve becomes worse as miners become commoditized, and as their hardware doesn't become obsolete, this curve becomes more steep, and as this ideal curve's gap becomes 600 seconds becomes much more quick. We think that a gap will be profitable at the next block halving, and this gap actually approaches 600 seconds far into the future. This issue is made worse by the fact that hardware is becoming commoditized.

There are some obvious security implications. There is increased vulnerability to attack. If a miner is willing to mine suboptimally, and start sooner, they are able to increase their.... We have some miners mining at some gaps, and some attackers starting earlier, which fraction of the real hashrate would they need to perform a 51% attack. As the gap deviates from zero, the fraction of hash power that an attacker needs quickly drops from 50%. This is a real issue and a real threat for the security of bitcoin.

A block needs to be immediately profitable to mine. An assumption by this model was that there was no backlog of transactions. The backlog of transactions needed to solve this issue would have to have enough value in it so that a block is already profitable to immediately mine. The most obvious is that users are going to have to wait potentially long periods of time to get their transactions into the blockchain. At Princeton we have released a bitcoin MOOC on Coursera, and the exact description of this backlog we're trying to explore in future work.

This mining gap is a real issue that needs to be part of the discussion of scaling bitcoin, and it becomes important when considering changing the block size. Find me at lunch and ask me questions.