Can the 51% attack be made to become 81% attack or 91% attack?

Question

Since the 51% attack happens if there are more than 50% of nodes that fake the data on the blockchain, can it be actually 81% or 91% that is needed to fake the data, because it would be much harder if more than 80% of the nodes are "bad guys".

So what I mean is, can it be the case that even 79% cannot be an attack, but need to be a higher number, such as 81% or 91%.

It may appear if the verification of data can reach a 50% level, reaching out to 1 more node of those 50% can make it become 80% to 100% easily, so one extra step is all it takes?

Answer 1

This question is based on false assumptions. The node network does not vote. It exists as a social consensus. The consensus relies on node operators to choose to follow the same rules. In some discussions this is referred to as "supermajority", which is accurate. It is completely inaccurate to believe nodes can vote, or that nodes can be reliably counted. All Bitcoin nodes are independent

The so-called 51% attack scenario is derived from the Satoshi white paper, under the heading "Calculations". This warns that a miner with more than 50% of the hash power can overtake all the other miners and mine blocks containing his own fraudulent transactions. The scenario is a consequence of the "longest chain" principle in the design. When there is a tied mining race, the node network will have a temporary chain tip fork, which is usually resolve din the next block, in favor of the longest chain. Nodes with the shorter chain will perform a chain tip reorg, to resynchronize. A 51% miner can simulate a tied mining race with hash power

Satoshi's scenario describes an attack which replaces one block at a time. The white paper includes some mathematical projections which display that it becomes exponentially more difficult to force chain tip forks more than one block long

It is now known that 51% hash power is not necessary, and that an attacker who shadow-mines a chain tip of multiple blocks secretly, in parallel with the regular mining network can create a chain tip fork of arbitrary length, just by winning one block more quickly than the regular mining network

Shadow mining scenario: acquire at least 15% of the hash rate. Mine in secret, in parallel, for an hour or a few hours. Eventually, the 15% hash power means a 15% chance of winning a block. Do not broadcast the winning block. Keep mining for 10 more blocks, and then broadcast the 11-block tip. The "longest chain" logic in the node software will recognize the attacker's 11 blocks as longer than the regular mining network, and will automatically reorg the chain tip

Attacks like this have been seen several times on Bitcoin Gold and Bitcoin Cash SV

Answer 2

I'm not sure I understand the question fully, but I'll try to answer anyways.

First, what a 51% attack is, is when a single miner controls over half of the hashpower on the network. If an attacker who had 51% of the hashpower wanted to attack the network, they would simply continue to mine their own blocks, and refuse to build off of blocks of any other miner, and because they control over half of the hashpower, their version of the blockchain, consisting entirely of their own blocks, will be the longest. The remaining 49% of miners won't be able to outrace them, and because Bitcoin considers the longest version of the blockchain to be the valid one, the blocks of the remaining 49% will become orphaned.

Because they can prevent any other miner's blocks from being accepted, they will be able to include only transactions they want in their own blocks, censor transactions they don't like, etc. since they control all new blocks.

As such, it's not exactly that the Bitcoin network is reaching out to nodes to validate transactions. Other miners simply can't catch up to the new blocks of the attacker, and so the attacker's version of the blockchain is accepted as "truth".

Answer 3

The 51 percent attack isn't necessarily "faking the data". It is generally referred to say including a double spend in a block that would normally be rejected by the network but the honest part of the network struggles to reject that block and the chain built on top of it because it has a minority of hashpower. The point being that proof of work is still completed, it isn't "faked". But in answer to your question, of course a 81 percent attack or 91 percent attack would be even more concerning than a 51 percent attack. It is called 51 percent because that is the minimum needed to pull off the attack.

There is nothing that can be done to increase the minimum of 51 percent needed to pull off the attack to say 81 percent in a proof of work context, it is the nature of the system. Of course, in reality the network may choose to follow the chain with reduced proof of work but without the double spend transaction in it. It would be disruptive, extremely expensive for the attacker and could (likely) fail.

Answer 4

Since the 51% attack happens if there are more than 50% of nodes that fake the data on the blockchain

It's not full nodes but miners and they do not attempt to fake data but reorder history of transactions in a "51% attack"

can it be actually 81% or 91% that is needed

It can be anything above 50% and not necessarily 51% in a practical scenario like CZ was considering in the Binance hack to reorg:

Jimmy Song has written a nice tweet thread and medium post about it. I will quote few tweets from the thread:

If 75% of the network going with this scheme, you would need on average 116 blocks to overtake the current chain, or about 1450 BTC worth of mining rewards. At 60%, this becomes 290 blocks or 3625 BTC. At 55%, 580 blocks/7250 BTC

7250 BTC > 7000 BTC, so at minimum, you need more than 55% of all hashing power to agree to reorg the chain. In 58 more blocks, this rises to 60%, in 116 blocks, 65%. In 174 blocks, 70%, 232 blocks/75%. The cost goes up pretty quickly assuming everyone agrees

https://twitter.com/jimmysong/status/1125977497047314432

You can read the medium post for other details: https://jimmysong.medium.com/reorg-scenarios-binance-hack-edition-849fc7e7df07

Also read Greg Maxwell's thoughts on "51% attack" to understand it better: https://bitcoin.stackexchange.com/a/101560/