Review of Section 1.1











The first sentence "If a miner chooses not to publish a block...the remaining miners will complete 2^ In this post, we critique Section 1.1 of Wright's paper. Its subtitle is "the Bitcoin process summarized" and begins with the following three sentences:The first sentence "If a miner chooses not to publish a block...the remaining miners will complete 2^

l

hash puzzles" is confused for two reasons:

The next PoW is indeed expected after an additional 2^l attempts are made, but the PoW may be found sooner or later. There is no guarantee that "the remaining miners will complete 2^l hash puzzles" nor is there a guarantee that if they did they would necessarily find a solution. The fact that the sentence is prefaced with "if a miner chooses not to publish a block" is misleading because mining is a memoryless process. A solution is always expected 2^l hash attempts from now.

The second and third sentences can be easily combined. A more precise way to write the quoted blurb would be:



Assume the selfish miner finds a solution for block height N at time t =0 and chooses not to publish it. From this point in time forward, the honest miners would, on average, find a competing solution for block height N after performing 2^l hash attempts, while the selfish miner would, on average, find a solution for block height N+1 also after performing 2^l hash attempts.

​

(10 min) * (1 - 0.5) / (0.5) = 10 min.

​

(10 min) * (1 - 0.01) / (0.01) = 990 min.

​

The honest miners will find a competing block on average in (10 min) / (1-α) time.​

(of course this is assuming difficulty hasn't reset).

READERS: Shall I continue, or are you convinced that the paper is fundamentally broken (the "5 min" error is enough for me to be convinced).

Although the author's writing is unclear, I'm going to give these first three sentences a pass. The next sentence, however, is nonsensical:I assume he is referring to the selfish miners when he says "miners," but what is? He says it's the "total computing power." OK so let's put some numbers to it. Let's first assume= 1,000,000 hash / sec. Then 1 / (1 - x) = 1 / (-999999) = -0.000 001. Ignoring the fact that we're getting a negative number, what the heck are the units? Clearly,cannot be the "total computing power."In order for the equation to be dimensionally consistent, x needs to be a dimensionless number. So maybeis some sort of fraction. Butis also the "total computing power," so the only reasonable fraction I can think of forwould be 1. In this case, 1 / (1 - 1) = infinity, and the equation still makes no sense.Alright, I give up. I have no idea what the author means by this equation and this sentence. Moving on...This statement is true if we assume that bythe author means the block time (10 min) and if we also assume constant network difficulty. However, this is such a well-understood fact that the author could just state it. It simply means is that if the selfish miner controls 1/2 the network hash power, he'd expect to find his second block 20 minutes after his first; if he has 1/3 the network hash power, he'd expect to find his second block 30 minutes after his first. This is basic stuff.The author's following sentence reads:This seems plain wrong. If we imagine the case where both the selfish miner and honest miner have 50% of the hash rate (= 0.5), this equation works out to:Why would you expect the remaining miners to findin 10 minutes? In this example, they have the same hash power as the selfish miner who doesn't expect to find a block for 20 minutes!If we test out the formula with= 1/100 (hardly any selfish mining hash power), we get:This also seems wrong. If only 1% of the network is selfish mining, why would it take the rest of the network 990 minutes to find two blocks! It's absurd.Perhaps this equation contains a typo. Moving on...The next sentence says:which is equally nonsensical because it implies that the honest miners solve blocks faster if they have less hash power! The correct statement is:Notice that I didn't reference this time to when the last block on the public chain was found? That is because it doesn't matter. Bitcoin mining is a memoryless process.It doesn't matter when the last public block was found; the honest miners always expect to find another block (10 min) / (1 -) fromAlright, moving onwards...The author hasn't even explained what the strategy is; all we know so far is that the selfish miner chooses not to publish the block for some reason. What exactly "seems to work?"Oh good, there's a diagram next. Maybe that will help explain things.Actually now I'm more confused. I thought the hidden block event was at t=0? Shouldn't the SM find blocks on average in 30 minutes instead of 20 minutes as shown? We also see that the author is again assuming the mining process has memory. The honest miners do NOT expect to find the next block 5 minutes after the selfish miner finds his. They expect to find the next block 10 min / (1 - 0.333) = 15 minutes after instead.The author still hasn't explained what the selfish mining strategy is yet, but has now made numerous errors.