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About the talk
Speaker: Rod Garratt
Rod Garratt holds the Maxwell C. and Mary Pellish Chair in Economics at the University of California Santa Barbara. He has served as a Technical Advisor to the Bank for International Settlements, a Research Advisor to the Bank of England and is a former Vice President of the Federal Reserve Bank of New York. During his time at the FRBNY he co-led the Virtual Currency Working Group for the Federal Reserve System. After leaving the FRBNY he consulted for Payments Canada and R3 on Project Jasper: a proof of concept for a wholesale interbank payment system. Garratt received his undergraduate degree from the University of Waterloo and his Ph.D. from Cornell University. He has published in the top economics journals including Econometrica, the American Economic Review and the Journal of Political Economy. He is an Associate Editor of the Journal of Financial Market Infrastructures, the Journal of Network Theory in Finance and the Journal of Public Economic Theory.View the profile
2020 Ford F150. I'd like to thank the organizers for allowing me to present this work. My title, is why fixed-cost matter for proof of work based cryptocurrencies? My name is right there from University of California, Santa Barbara, and this work is joint with Martin been ordered from the Bank of Canada. This paper is motivated by an event that occurred in May of 2018. When a spin-off of Bitcoin called Bitcoin, gold was hacking, a rare 51% attack now, this, which is surprising to me because when I was working at the New York fed several years earlier, I had written a blog post that
basically argued that it was very unlikely that attacks Whittaker on bitcoin. And so I was very curious as to why this happened and I was out working at the Bank of Canada at the time from from UCSB end and we speak with Martin van or exactly happened in the Bitcoin. Gold was born as a hard Fork of the Bitcoin blockchain in October of 2017 and use the proof of work protocol that disable the use of specialized equipment in particular, Application-specific integrated-circuit Asics operations. And the goal was to achieve higher level of
resilience centralized buying structure with a comment that I made and in the white paper, which is it, every CPU is equally important and this is articulated in in in Bitcoin gold. Org says, that the goal was to bring Bitcoin back to the people. So there was this general idea that by having a six chips mining was becoming too specialized that the average person couldn't mine and that we should reinstate. This essentially is democratic aspect of mining in Bitcoin gold
16 to 19 and $18 worth of gold. Loss of confidence in Bitcoin gold and large decline in the exchange rate. In fact, like the less than 1. So we take a look at this chart. What we're doing here is is a Time Zero with when they the attacks and so you see that it's in the days, following the attack, the price fell in terms of dollars but then something might have been happening to cryptocurrencies in general. So the blue line is showing the price drop in terms of Bitcoin.
So specific So the question is, why was Bitcoin gold subject to a successful 51%? And what we are you in this paper, is that understanding the role of fixed costs. And cryptocurrency Mining is crucial to answering this question in and do a quick tutorial online. Audience will let me Begin by just talking about cryptocurrencies, they store transactions in blocks. And what I'm showing, so, here are enjoying a sequence of blocks, the history of all transactions that have occurred. And here we see a new block that includes a payment from Alice to Bob. And in the future, new blocks
will be added and supposed it occurs to us that she would like to use the coins that she paid the Bob in order to buy something from Charlie. Well, she can't because the history shows that she already spent those coins. So what she would have to do, in order to re spend those coins, is to rewrite history. So she would have to go back in time before that transaction to Bob occurred. And she could consider paying the coin to Charlie or maybe just to just to herself at a prime. Well, there are two obstacles to this the Bitcoin rules. Say one is that in order to create a new block, you
have to solve a crypto graphic puzzle, and this requires, and it's very difficult to do when there's a lot of lining up our associate with the network and you have only a small amount of that. My power is very difficult to be hot and secondly, the protocol says that that minor should follow the longest chain on whether or not they having a second. Even if you're able to stall the block and in bed, this new transaction. I will no longer be valid. So the question is, is it worth it? And so, the what we do
is we look at the benefits of doing this, double spin. So essentially that's can be measured in terms of how many queens you're able to spend. And then also the costs associated with this double standard fact, that what are they come from? Come from the fact that miners are paid a reward in terms of new coins? It's offered by the protocol and also some rewards that come from transaction fees paid by users. And so if there is a impact on the Bitcoin price, as a result of the attack, as I showed us are the Bitcoin gold price
as I showed her earlier than the revenue that you're going to earn from your existing mining equipment is going to drop, so there's going to be a potential loss during the time of the attack on here and there's going to be a potential loss. The potential cost of the attack to the potential benefits. Much of what we're going to say because this is important to fix cost and sockets exclusively on is the electricity cost or some people have a factory in depreciation of equipment.
There are some exceptions. There's a paper by that models. Bitcoin mining in terms of a flow Cosmic but there's a discussion of office Carson and correcting What He suggests and then pride and Walter they do. Look at fixed costs and there's only six but they don't. So this just by way of interest, is an example of a spreadsheet used to create a theorem and what it basically, all the graphics cards in the cost of all the other equipment at a significant relative to the electricity
and made it that two-thirds of the cost of Bitcoin. Mining are fixed costs. Okay, so what we incorporate fixed costs into the analysis. Here are some of the results. So the first result is this basic idea what wires make zero profit. So typically equilibrium only variable costs then. We'll be true. Miners will make zero profit if the price Falls than miners will simply leave and stop Mining and so they'll always be making zero profit. Now, if we introduce a fix,
then that's no longer true in a long-run equilibrium miners, makes your profits but exchange rate fluctuations are going to cause them to make short-term gains or losses. So minor do minors lose when the exchange rate drops will know if they're only variable. In the case of fixed costs, you don't exit right away. So some people do their losses does mining power exhibit, downward virginity. In the case of variable costs true, in the case of fixed costs, that is you don't leave right away. If you have fixed costs, it essentially, this is the idea that
once the price drops, you may not be covering all your class anymore, but as long as you can cover some of your variable cost you continue to mine and then this idea of what's the cost of a large amount of attack. Lowers the value of that mining equipment makes attacks more costly, so that's another aspect of changes and we'll talk or I'll talk about Okay, so before I go on into the formal analysis, I just want to say a little bit about an extension with two cryptocurrency groups with transferable mining power
essential my awesome cryptocurrency to mine, different cryptocurrencies. And so we have to take that into account whether or not, that's possible. So that's very difficult with things like big going, but it's much easier to type of mining. Rigs are used to mine. For example, and we show when we consider groups are transferable 90 powers that the results are unchanged, when the exchange rate of perfectly exchange rate, correlation transferability can eliminate the protection that fixed on Spotify.
also, we will, we will provide you with some empirical results that support the theory that I So let me know I'll get into the theoretical model. So the main variable or what are the main variables, is the exchange rate to read the note that by ass. So that's measured in terms of dollars per Bitcoin exchange rate, The remaining benefits for blocks all we're going to know by Bea. So that's the, that's the reward. There's a peer. Cost of mining of operating a mining. You at that, step salons. That's the variable cost. There's also a fixed cost and crucially, there's also a
real True Values, what you can sell your mining equipment for if you desire decide to stop mining. So think about something like Bitcoin which is mine was specialized A6 chips in that case, if you're not mining Bitcoin, those chips are not good for much else. And so the guy at the video on front of you, thought you would be close to zero, whereas some cryptocurrencies can be mined with graphics card for gaming. So, they have a reasonably High alternative Hughes value, and then some cryptocurrencies could be mine with a standard TV use.
Alternate, it's very high close to the original fix cost. My Powers been noted by the variable Q, that's the total money power that's being implemented. On the network, can use it at the moment and then we call the mining difficulty HUD. That's the total amount about his money power, that required to deliver one block up four. Finally, the cost of capital is our that's that if he thought of as the discount rate. So what we do is we model the arrival of salt blocks. To
remember, everybody's minding, there's a certain amount of money power out there. They're trying to stall the process. That essentially has a random success rate and so we're good old model. This as a process where the arrival rates all by one mining unit equals one equally good End of cappuccinos. The stochastic number of blocks that are sold by a single mining unit. The top rating for cheaper is so the compute the expected present value of a single mind unit till.
T and that's the formula at the bottom of the slide. So the idea why your ward? So if you want my number of a blocks, you're going to Salty, K cereal, the arrival right around 9:40. We're going to, we're going to be successful, basically one over QT, * 4. And so this whole formula quite simple, right? This is just standard discounting by the way. So, we get this formula, which gives you the expected present value of operating, a mining unit for 2. Okay.
So we make one simplification the main text of the paper, which is that, we just imagine that the mining unit last forever. So we just take T to Infinity. So then that then the mining Revenue that you get SB over 2, minus the cost. Epsilon, this is just a perfect perpetuity, so it's just divided by the discount rate are and then we subtract the fixed costs. This simplification is easy to undo end in the paper. We actually show exactly what happens to these calculations. If we allow, find the mining equipment, only lasts for a finite number of periods. But for this presentation, I'm
going to do the event, like this is just a little bit. So it's profitable than to install until the mind power in the network, it's this level. So basically, the idea is that profit should be zero and so we can solve for the optimal amount of money power in the network that lets these profit equals 0. So that's our cue so, the standard formula So after nyberg stock exchange rate of Ella person, so we think about a Toby think about if the revenue used to be s x be so that's dollars per Bitcoin con Bitcoins or whatever.
Then we're imagining that if Al would say 10% of that revenue is now only 90%. Equilibrium condition is no longer ago going to hold. We're no longer at zero profit but my nurse will continue my name. So long as they're still covering fixed costs or variable costs. Money props are still Do supposed to rain in equilibrium solve for a critical loss. Critical percentage drop in the exchange rate at which point points. Not saying it. So it depends on through the overall type of So, if we were to look at that in terms of a graphical picture,
the idea is that let's first of all, look at the case of general-purpose Hardware. So you can just use your CPU to be the same thing. Is there being no fixed costs because I need to put you have you been just instantly sell for what you pay for it? If there's if there's any kind of a loss, this is the percentage of loss on the horizontal axis lining power, just dropped or simile. In other words, if they are the Other Extreme. If we look at something like Bitcoin mining where the alternative used value of the money equipment is 0, then there's no response to a do, do a
drop in the exchange rate to the percentage loss as to get all the way up to the point where you're better off. Just stopping, you're no longer covering your variable cost at all. And then there's an intermediate case where you can sell your mining equipment for some alternative use value V, that's between 0 and ask. So, in this case, you don't respond when when there's a lost, but once that lost brings you to the point that you're better off, selling your graphics cards, The Gamers, you go ahead and do that. And so that same thing can be shown in terms of what's happened to the present
value of your remaining losses in the drops in the exchange rate have no effect on you. If you're using a CPU, the present by your equipment, is it always the same? You can always sell it for what you paid for. Otherwise I can drop as low as me or you can drop all the way to zero in the case of an A6 chip. Okay. So what are the implications of this locations of this picture? If I go back to hear, it says that when we see drops in the exchange rate, we expect to see immediate responses in the case of either no fixed costs or cases, where their sticks cost for high Outrigger you
spell you say chips in her mind with CPUs two drops in the exchange rate for chips that are mind using 1/6 chips and that's what we do. So what you're looking at here is a regression that we ran. So we were we want to look at the relationship between changes in lighting power to, we do this in laws and changes in the exchange rate to Jessica levels are are integrated of order one but first difference, And what we, what would we expect from this direction. So this is the change in the amount of money card at used in the network. This is the change in
the exchange rate. This is the change in the, in the box. So this is looking at, this is zero and less. We we reach the new Max during the current. T-72 in which case we we see that change and then we also include a dummy variable for whether, or not they're hounding Paddington block rewards at 10 to drop and a half. Every certain number of a block that are awarded So we can talk about or value is equal to fix cars or something like CPUs. Then we would expect you to move perfectly with Delta ass and this term
would be insignificant on the other hand matter, then we would expect. We would expect it that that the changing she would not be responsive to changes in lighting power button, but it would only be responsive to changes in mining power to change a power, would not be responsive to changes in the exchange rates. But the changes in mining power would be responsive. If the change in exchange rates brought you to a new, a new Max above you. Okay, so here's what we see in the regression. So what do we
do here? We look at these five different cryptocurrencies. What was the criteria? Well, the first criteria was that there's at least five million dollars in market cap for the coin. And if there was more than one, we picked the largest point for this analysis, We wanted a three-year history. Both price in mining data. No significant change in the algorithm. It was used and we also wanted the span of a variety of different protocols. So the protocols that are used here are sha-256 for Bitcoin at hash refereum script for Litecoin a
Kryptonite from your own x 11 for cash, Bitcoin is the one that uses the A6 chip, which is the most specialized and dash uses a protocol, which is a combination of a number for like a CPU. Where is it. Some of these others are more intermediate. Until the results are pretty consistent with the theory. So as I mentioned it fixed cost matter, we only expect the coefficient on the max On The Backs change in the changes in the exchange rate to bring you. And that's exactly what we see. The changes in the exchange rate that
we see that there is a significant variation, just a regular changes in the exchange rate, with the changing my power and the end changes. And then and then the theory of the somewhat mixed, but that makes makes sense. Because he has a protocol that has a reasonable alternative. Okay, so now I can move on and talk a little bit about what this all has to say about double-spending attacks. So the formula I have here is showing you the remaining in the cost of an attack is successful after two periods to the attacker. So what we have here is
we have the two components that I mentioned early on, in the talk. So first of all, there's going to be impact on the money rewards during the attack. So again the idea is that you are going to do a double spend. So you're going to send a bunch of coins. Do an exchange and transfer them into something else, and then you're going to be getting this process of trying to solve a sequence of block, so that you can construct the chain. That's longer than the existing chain that followed after you made your original transaction. So now during that time there's going to be a number
blocks that are that are solved in and had you just continue Mining and not going to attack, you would have been collecting rewards for the for the blocks that you were sold during that. But instead you're doing all this in secret, when you created a new thing that you can amend that to the cryptocurrency, what you're going to get those out of the loss that occurs from that on. So if you've done save an expectation, you would have done some permanent damage to the currency. And so all the equipment that you have this going to
mine Bitcoin from that. Don is going to earn Allure return. Okay, there's the Lost X. The turn. Okay, so then what we have is we have a simple economic formula which determines whether or not we should undertake. So on the left, what we have is we have a number of coins that the attacker is able to spend. This is just saying that the greater than the, than the cost of the attack. Alan. This is just that formula written out in long form and this is useful because you can take a look if you if you go to the paper you can take a
look and you can see how whether or not this racial was mad, that is how many coins you want to spend to create a double spend attack, depends on the other parameters in the mall. So that's interesting. This table is the and sometimes the summary table for this presentation which shows you what to make of this, what, what does introducing fixed-cost, how does it that impact the way? We should think about the likelihood of a double spend? And so, what do you think about moving horizontally? So
things basically in the table, there they're getting The attack is more costly as we move to the from left to right and were costly as we moved from top to bottom. So what we're showing in the top here is the percent drop in the exchange rate, for the bigger, the drop in the exchange rate that results from the more costly it is for you to attack again. You have all this equipment. If you kept using it, you would be earning an exchange rate for forever in the simplified model, but because you attack your, you're going to lower that exchange rates. Are you going to class? And
these are just three possible estimate for what that drop is 50% bigger, the drop though, the more costly the attack is going to be on that Dimension. And then on this on the vertical Dimension, it's it's how valuable is the, what's the value of the alternative use of the mining equipment? So if you can sell your mining equipment, for 100% of what it's worth, then you don't really care. If you damage the value, you can just sell the equipment. Call, you don't care in terms of a long run as you'll sell the equipment. After the attack, this is equivalent to the air is being built
that. You would need to be able to make it this into context, estate Bitcoin, what we show my choices are here so you can ask yourself that you can use the type in your own printer or values that you think apply to a particular coin and see what the results are. We spending over to be worth it to engage in a double spending and tax? According to their values, we chosen here in this for the best-case scenario where you're using say CPUs and there's only a small impact on the coin price. You would only need to use 60,
60 coins but in something like, Bitcoin where there is zero alternative, you spell, you, and maybe a thousand points. So, most people don't have. And I am an exchange took an order from your cell, or large, it would have lots of Rice and media media Exchange. Our Awards have gone to 0. So the only thing you now get for the protocol. So the only thing you now get her transaction fees, and the reason we think this case is interesting, it is because many people have talked about whether or not Bitcoin is doing once rewards, call
200. And so there is zero, it could take months before, Bitcoin payment is final and less new technology is employed. So the idea is that 140 because accident analysis, which They believe that changes, if people who accept Bitcoin will have to set the confirmation. Be incredibly long in order to protect themselves. So in other words, what we find in our analysis is that if Bitcoin rewards drop to 0 so you only get transaction fees then. In this case, where there are no fixed costs in the low impact, on the exchange rate, you would only have to be
able to double space for Bitcoin in order for an attack to be profitable. In other words, the tax would be very profitable and so you would need to extend the confirmation number is that well no one uses specialized A6 Jeff's. So the value of 0 at 15% or even a larger dropping the exchange rate. So I think if Bitcoin was successful but the idea is it you need on the order of 10,000 I'll be going in order to be willing to engage in a successful double-spending even when the block
and I think maybe a little bit of irony here, is that in some sense, many people have criticized, there's a sense in which this is is, is not very, you know, I use the word Democratic what I mean by that is that it is not. Everyone is able to participate in this special feature, a Bitcoin, makes it safer than virtually any other cryptocurrencies more secure. So now to conclude, let me just point out that what we do in this paper as we accounted for fixed costs or we point
and is crucial to understanding both mining behavior. That is how changes in mind power, very with changes in the morning Friday and they're in the cryptocurrency price and we show it what the implications of this are for double-spending attacks. What I called the basic truth or what we call the basic truth, which is it Asic mining, which involves 6 cost in a low value. Reduces the profitability of Properties of mining hardware and the historical exchange rate path. I have
important implications for the number of block confirmations bunch of require for diets that comes out of the paper. And as I mentioned, really on our analysis, extends to transfer, paper to the Discover more about what we do. Thank you very much for your time.
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