This is one article in a collection of 52 articles published weekly throughout 2023 on the basics of Bitcoin. The series is intended for people unfamiliar with Bitcoin or people wishing to enhance their understanding of the fundamentals that underpin the technology. Please contact us, if you have any questions or comments.
As we discussed in our previous publication, the way the Bitcoin network determines which chain, among contradicting chains, is the correct chain is looking for the longest chain. If a person is wishing to attack the longest chain, the attacker will need to create a new, longer chain with different transactions to cause the double spend scenario to occur. For the attack to be successful the attacker could have the ability to have certain transactions in the new, longer chain that send coins to alternative addresses than was reflected in what the Bitcoin network previously deemed to be the longest chain. However, the attacker will only be able to intentionally “double spend” coins the attacker or an accomplice has under control and the attacker’s new chain will have to go back to the blocks it wants to change. This requires a staggering amount of computing power and would be extremely expensive.
Previous projects by the cypherpunks were unable to overcome the double spend problem or the Byzantine generals problem as it is more commonly referred to in computer science. This problem stated most succinctly is to make sure an individual cannot spend his/her money, or in this case, bitcoin twice. While Satoshi did not solve the problem definitively, he did create a solution that solved the problem to allow the users of the Bitcoin network to successfully utilize the network with close to mathematical certainty that the double spend problem would not be an issue.
In section 11 of the Bitcoin white paper, Satoshi discusses the mathematics of an attacker with 10 percent control of the Bitcoin mining network and 30 percent control. Let’s review the numbers using the more extreme example of an attacker having 30 percent of the Bitcoin network’s computing power. In this scenario, an attacker who wishes to attack the network with a block 15 blocks prior in the backchain (2.5 hours approximately in blockchain time – 15 blocks * 10 minutes = 150 minutes) will only have a 1 percent chance at success. However, the miner with nefarious intention will be foregoing the opportunity to mine the next block which the miner would have a 30 percent chance of achieving. Miners are currently rewarded 6.25 bitcoin plus the transaction fees associated with the block. A nefarious miner with 30 percent of the computing power of the Bitcoin network attempting to change transactions 24 or more blocks prior to the current block would have a less than a 1 in 1,000 chance of a successful attack.
Section 11 of the white paper includes a chart which shows how many blocks down it would take for a nefarious miner to have less than a 1 in 1,000 chance of a successful attack based on the nefarious miner having an assumed share of the Bitcoin network’s computing power.
| A Nefarious Miner Has Less than a 1 in 1,000 Chance of a Successful Attack | |
| Bitcoin Mining Power | Number of Blocks |
| 0.1 | 5 |
| 0.15 | 8 |
| 0.2 | 11 |
| 0.25 | 15 |
| 0.3 | 24 |
| 0.35 | 41 |
| 0.4 | 89 |
| 0.45 | 340 |
As the chart above displays, as the nefarious miner’s share of the Bitcoin network’s computing power rises, the number of blocks the miner can attack with less than a 1 in 1,000 chance of success rises. However, garnering that much control of the Bitcoin network hash rate is hard to fathom given the competitive, decentralized nature of mining and the hash rate continuing to rise in spite of the price of bitcoin falling.
While the Bitcoin network has never had a successful 51 percent attack performed against it, other cryptocurrencies have been impacted by such attacks. Ethereum classic was successfully attacked in 2019 and Bitcoin Gold was successfully attacked in 2018. However, the hash rate of the Bitcoin network is exponentially higher than any other cryptocurrency utilizing a proof-of-work system. The Bitcoin network’s hash rate as of February 27. 2023 was 288,927,289 TH/s. Bitcoin’s hash rate is exponentially larger than these and all other cryptocurrencies. This ensures the security of the Bitcoin network and allows users to confidently transact using bitcoin without the fear of a 51 percent attack or the double spend problem being an issue.
