# Maintaining the Integrity of the Blockchain even with 90% Maliciousness

Blockchains are prone to 51% and 67% attacks depending on its consensus protocol, which means if 51% of miners are malicious then the blockchain network is compromised or hacked. The same goes for 67% attack.**For the case of Bitcoin**, if malicious miners control 51% of computing power then, the network is compromised.**For the case of Ethereum**, if malicious miners control 67% of the nodes, then the network is compromised.

Depending on the consensus protocol used in the blockchain, the 51% or 67% attack can be in terms of computational power (Bitcoin) or number of nodes (Ethereum 2.0)

Now, the limits are pushed, and it is no longer 51% or 67% but is 91%, which means the blockchain network is compromised only if the number of malicious miners in the network are more than 91%

## How?

This is based on “Hypergeometric Distribution” which in turn is based on randomness and entropy. The below equation explains, with 90% malicious nodes in the P2P network, with 10^-9 probability of error, with number of nodes (N) tending to infinity then only 200 nodes (randomly elected) out of N nodes can validate a transaction.

Where, N is the number of nodes, 0.9 is 90% malicious nodes, 0.1 is 10% good nodes, n is the number of validations, p = 90001 (the probability to have at least 1 good node), 10^-9 is the probability to not have 1 good node in the 200 selected nodes (aviation standards).

In simple terms, consider a village of 100,000 people, with 90000 liars and 10000 truth-tellers. Alice and Bob are citizens of the village.

When Alice sends Bob 10 units (of some currency), the transaction is validated by **randomly** selecting 200 people out of 100000 people. The hypergeometric distribution ensures that in the 200 randomly selected people there is at least 1 truth-teller and that truth-teller will ensure that the transaction is not falsified/hacked and also makes sure to eliminate/banish the 199 liars.

**This is not only the safest and secure blockchain, but also highly scalable since just 200 nodes are needed to validate a transaction**