Proof of Work – Why would an attacker need 51% mining power to overtake a blockchain?

In a race, an athlete does not have to run faster than 50% of all athletes combined. he just needs to be the fastest.

Mining is not like race. Racers advance towards the finish line and the fastest racer ultimately wins. However, there has been no progress in mining Bitcoin. Each attempt (hash) either finds the correct block or not.

Bitcoin mining is therefore like a game of rolling dice, with a random Poisson probability of success on each trial. Higher hash power means more attempts per second.

If you want to reliably beat the rest of the network (i.e. 51% attack), you need more hash power than the rest of the network (i.e. you need to control 50% of the total hash power). there is). network).

Thus, we have miners M1, M2, …Mn and mining pools P1, P2, ..Pm in the network, with Pi (1<=i<= m) が最高のハッシュ パワーを持つ場合、こんにちは、私は不正なマイナーです。 (またはプール) は、個人的にサイドチェーンに取り組んでいる場合、最終的にネットワークの残りの部分よりも速くブロックをマイニングするために、マイニング パワー Hx > Must have Hi.

To attack 51%, Hx > ((H1 + H2 + H3 + ... + Hm) / 2).

only consider if Hx > Hi is not enough. Hi This is not the only other entity mining. A miner with any amount of hash power can get the next block (with a probability proportional to their share of hash power). Therefore, all miners must be considered together in the calculation.