Really like this idea.
Not sure I follow, could you give us an example of an attack?


You could. But this would just be a new (and less potent) variation of selfish mining, which is only applicable "if a block is announced with a bad time" (which would happen a lot less often since  nodes will be incentivised to keep their clocks accurate. More importantly it would not be a profitable strategy (compared to following the protocol).

I know that there has traditionally been reluctance to assume accurate clocks (since NTP is seen as a central point of failure), but this appears to me to be a very weak dependency. Even if you had the magical capability to change the clocks on all network nodes when you want (not when they choose to sync) to whatever time you want (typically the time that is in the header of your selfishly mined block) you only end up with a selfish mining attack which we are vulnerable to today anyway. So as far as I can see no worse attacks become possible and the one we knew about becomes immensely harder. But this could just be a failure of imagination on my part. 

Careful, this means that in the presence of a selfish miner attack, anyone can DOS the network by sending thousands of tiny (in both kB and BTC terms) zero-fee transactions. Huge blocks stuffed full of these garbage transactions will win the transaction-seconds comparison against smaller blocks containing only normal transactions and once there are enough of these txs in the network to push us up against the block size limit, it becomes ineffective against the selfish miner attack anyway.

This can be alleviated somewhat by using transaction-fee-seconds as gmaxwell proposes, but even then, an attacker could build a maximum-size block that contains a bunch of insanely-high-fee transactions that it created itself and is keeping secret. As soon as it successfully builds a block, it publishes all the high-fee transactions, but not the block. This allows it to win any tx-fee-seconds races with competing blocks.

Stop fighting a straw man. I never claimed that ASIC prices would be unaffected, just that this is immaterial to the decision of an atomistic miner.

ASIC values are pretty tightly coupled to bitcoin prices, but you know what is coupled even more tightly to bitcoin prices. bitcoin.


Reread that last sentence. In the absence of confirmation bias, you argued that even miners that were heavily invested in bitcoin would take part in an attack, since they were atomistic. Now you argue that atomistic miners that are heavily invested in bitcoin mining equipment won't take part in an attack. Why are the miners more easily swayed by the mining equipment that they hold  than by the actual coins?

Errm, any correct one will do. For someone who passes himself off as a source of game theory knowledge it is more than a little embarrrasing to get the payoff matrix for the prisoner's dilemma wrong. If you can't see a problem with the matrix in your paper I suggest starting with
http://en.wikipedia.org/wiki/Prisoner's_dilemma


No, for the hundredth time. I fully accept that a successful attack will destroy bitcoin, as does the atomistic miner. The atomistic miner hopes to hell that the attack fails,but takes part anyway, since his contribution is too small to make a difference between success or failure. This can also be stated as :


Nice.

"When you have no basis for an argument, abuse the plaintiff."
— 'Cicero

No, it is not. I am tired of explaining why, but you clearly did understand this in the past.

I'm sorry but your whole argument is flawed. You need to treat miners as atomistic and you don't. That invalidates everything that follows, so I don't need to read any further. Rewrite your paper while sober. Remove all consideration of the possible effect a successful attack could have on the value of the miner's assets. Get the payoff matrix for the prisoner's dilemma right, and then try again.

And I've got the same thing AGAIN. Here's the raw tx from gox. Double spent. What a bunch of incompetent fools.

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Huh??? Are you drunk? I have been selfish mining with my CPU for the past 30 seconds, so I guess we're all F#@#ed now. Sorry guys, I must have misunderstood something somewhere.

That graph is transactions-per-block which you would expect to go up if there are more transactions or fewer blocks. However, no corresponding increase is visible on this graph of transactions-per-day, suggesting that there are indeed fewer blocks being produced. This has to be a sudden drop in hash power or variance. My gut-feel is that the swing is too large to be explained by variance, but one would have to do the math to be sure, preferably using only block times from after the OP to eliminate sampling bias.

It ABSOLUTELY mattters. If miners are atomistic, then your entire argument falls apart. Take for instance :


The miner considers the probability of his hardware dropping in value as being independent of his decision to join the attack or not. Any subsequent consideration of hardware value when making the decision to mine selfishly or honestly is an error. The only way that this is not an error is if you claim that miners are not atomistic. But that is equivalent to saying that bitcoin is not decentralised.

Interesting how you are "right in both cases", but when others use the same assumption, they are "incompetent" and have a "fundamental misunderstanding of the incentives".


If you assume that miners are atomistic, then the size of the investment is irrelevant, because the miner assumes that the attack will succeed or fail independently of whether he cheats. Therefore ANY consideration of the attack's impact on the valuation of any of his assets is erroneous. It is like trying to consider the effect of a possible crash of the stock market on my net wealth, when trying to decide whether to have egg or cereal for breakfast. Erroneous, not because I will be able to offload my shares fast enough, but for the more fundamental reason that the market will do what it does, for better or worse, irrespective of my choice of breakfast.

If miners are not atomistic, then bitcoin is not decentralised.


Nope, not really, I wanted to use the atomistic assumption in a counter-argument, but I couldn't remember where I had seen it defined. Forum search and voilla, guess who?

Sorry man, but you are embarrassing yourself now. There is absolutely nothing wrong with their conclusion under the common game theory assumption that miners are rational and atomistic. If bitcoin mining truly is decentralised, then the atomistic assumption has to be true. A really smart guy who is worth listening to when he is not in full-on confirmation bias mode explained it as follows :


Similarly a rational atomistic miner will neglect the effect his selfishness will have on the bitcoin price or the value of his mining hardware. He is simply too small to matter and the price is unlikely to be affected by his individual action. Even if he believes that the price will be affected, the net gain can always be made positive by holding a sufficiently large short position.

Work can be wasted whenever orphan blocks are produced. Orphan blocks do not contribute to network security, they do not pay their creators, and they are not relayed to the rest of the network.



If you are trying to achieve gamma=1 then yes, the signal that you need to act is also the signal that you have already lost. But unless I am the VERY LAST node on the network to receive this block, it may be possible for me to get my block to other nodes that have not yet seen the honest block and in this way recruit at least some of the honest miners to work on my chain. Even if you do not agree with this seemingly obvious statement, it DOESN'T MATTER. Because as I am getting tired of pointing out, the attack still works for gamma=0. This is the case where we assume that I was indeed the very last node to receive the block and not a single honest node will compute a single hash on my block in the case of a tie. In this magical case I need 33% of network hash-power to earn excess rewards.


Nope still wrong. In my simulation, nodes get allocated to mine on one block or the other with a probability of gamma of being assigned to the attacking block (you've got the logic of gamma reversed by the way) and I replicated their results perfectly. What is more, for the interesting cases gamma=0 and gamma=1, the two approaches are exactly the same.

I don't really want to argue this point. As I have repeatedly stated I think that gamma->1 is extremely pessimistic and probably not achievable in the current network. But that is a red herring. The fact is that gamma->0 is extremely optimistic and even under those circumstances, the attack works. No Sybil attack is needed, so I wish we could stop discussing whether the Sybil attack is possible.

Yeah, I eventually got mine to go through. Allthough the first few that "went through" actually didn't go through at all but were double-spends by gox (see thread on this elsewhere). I strongly suspect that the theory that this happens when gox's hotwallet is empty is spot-on. This happens whenever the gap between gox price and stamp price is narrower than usual. You get a run on withdrawals at gox which results in an empty hot wallet. Count on this taking ~2-3 days to resolve. 

And the "cave" or the countermeasure in this case is that one or more of the honest guys should bleed money operating a PPS pool at a loss until the attacker goes away. Errrm, yes that sounds like it will work.

.Yeah, I feel the same about NP!=P. I could probably solve it in an afternoon if I put my mind to it.


As stated earlier, I agree that the existence of PPS pools makes this attack much less viable. But the existence of (reasonably priced) PPS pools is an assumption. Nothing in the protocol requires or guarantees it.

It may indeed be possible to build a better mathematical model of this than they did. It may indeed be a much better use of the time of someone who is "qualified for it", than bashing the model that they put forth. But the model that they put on the table is vastly better than what we had before to describe this strategy, namely some hand-waving. Disagree? Was the 33% figure known before?


And if the pool doesn't reach 51%? The selfish mining pool provides larger payouts from day 1 (or at least from the first time that 33% is exceeded. So there is no need to trust the operator for anything beyond your next payment. And what exactly are the upfront costs of the selfish mining strategy that you refer to? BTC-Guild could implement this today with a few lines of code. To be clear, I don't think it would work. If they tried that it would probably destroy their business. But I don't see the up-front cost.

No, you don't need to get to 51%. IF you do then you can control the network. But even if you just have 40% of the hashing power, you can make outsize profits and push other miners into loss making territory, which very likely gets you to 50%. But recruiting/buying 33% of the network hash power and relying on economies of scale to get you to 50% is very different from simply recruiting/buying 50% of network hashpower.

If I boot up my multi TH mining rig and start mining blocks from the genesis block onward, is my work not wasted? Does it contribute to network security? Will I earn any block rewards for the blocks I mine? As far as the rest of the network is concerned, I might as well not exist.


I have taken a look and cannot for the life of me understand what is confusing you. Gamma is defined quite clearly:"We denote by gamma
the ratio of honest miners that choose to mine on the [selfish] pool's block, and the other (1-gamma) of the non-pool miners mine on the other branch." The variable is consistently used with this meaning. And your assertion that "the evil miners have magically found a way to detect the competing block in the honest miner's memory, before it has begins to spread on the network." is plainly false. The situation that you describe would correspond to a gamma of 0 (the worst case). But even when gamma is 1 (i.e. "the honest miners have magically found a way to always work on the honest block in the case of a tie") the attack works for an attacker with >33% of network hash power. I find the researchers' claim that a gamma of 1 is attainable by an attacker in the current bitcoin network to be tenuous at best, but this is not that important, since the attack works even for the best case where gamma=0.



BS I replicated this result and I can guarantee you that the mining function is not deterministic. Besides, your premise is laughable. How accurately can you really read that chart? Enough to say that the simulated results are within 1% of the predicted values? 0.1%? You can easily get simulation results accurate to a fraction of that in a modest amount of time on a dated single core machine. I know because I tried.



Strawman. Nowhere on page 13 do they suggest that or anything that I can interpret as being equivalent to an attacker being required to "insert itself between every other node on the network". If you disagree please post the relevant quote. As stated earlier, I find their assertion that gamma close to 1 is attainable to be tenuous, but this is just a misrepresentation of their position.


Real mature. This is peer-review, is it?

Don't quite agree with you here.
1)  Agreed
2)  Agreed. But it is important to note that the selfish pool suffers smaller losses than the others. Therefore rational wealth maximising agents who denominate their wealth in BTC would join this pool (were it not for your observation under Fail B which I will get to next).
3) The lower difficulty is open to all, but the other pools are still underperforming relative to the selfish pool. Rational miners still join the selfish pool. It is entirely possible that another selfish pool starts up, but far from being a threat to initial selfish pool operator, it is actually the best thing that could happen to him. Since the gains grow superlinearly both pools will mine more coins by joining forces than they would have otherwise. This process runs away and leads any pool  that starts with >33% to end up with >50%, at which point the classic 51% attack becomes possible.


THIS is a critical observation, which I have not thought of or seen mentioned elsewhere.  Essentially PPS can invalidate the entire attack, since a rational miner would rather join a PPS pool, where he will earn even more income than from joining the selfish pool. One can reason that the PPS operator, (who takes the hit for all of the orphaned blocks) will cancel the service or put the price up enough to compensate. But this means that the attacker first needs to keep the attack up for long enough to drive all PPS operators out of business. Only when this is complete will rational miners flock to join the selfish pool. This makes PPS operators vulnerable to this attack, but it is not very different from the well known block-withholding attack that they have always been vulnerable to, in fact it is a little less serious since it can easily be detected. Also, if someone with deep pockets (Bitcoin Foundation? BTC guild?) publicly commits to keep at least one PPS operation afloat for the duration of any such attack, then the selfish pool attack suddenly becomes very unattractive indeed, since you need to incur a sustained loss (relative to what you could have earned with the same hashing power at a PPS pool), and only if you can sustain this loss for longer than the PPS operators can sustain the loss you are inflicting on them can the attack actually start recruiting other rational miners to help you. This is somewhat analogous to trying to enter a new market against an entrenched competitor who is committed to a strategy of predatory pricing i.e. they will sell their products at a loss until you eventually go bust or leave the market.


I actually think the paper is quite good. The attack is quite unlikely to work in practice, but the theory is incredibly important. The result  is counterintuitive, but undeniably correct. I've done my own calculations and simulations and arrive at the same results as they do. Some claim that the attack was known before, but I am afraid none of the rather vague hand-waving explanations of a mining cartel attack has managed to convince me that this is possible. The fairly basic math used in the paper convinced me in less than an hour.