Ethereum: Does the Bitcoin Blockchain Solve the Byzantine General Problem?
The Byzantine General Problem (BGP) is a complex computational puzzle first proposed by Dimitris J. Christodoulou and Silvio Micali in 1980. It is a challenging problem for Byzantine Networks (BNets) that concerns the collective behavior of nodes on a blockchain network, including Ethereum. BGP states: given a graph of multiple nodes, determine whether it is possible for at most two nodes to agree on a given value.
Bitcoin Blockchain and the Byzantine General Problem
While the Bitcoin blockchain solves some problems related to Byzantine Generals, such as the difficulty of solving a linear congruence equation (a form of BGP), the main Ethereum blockchain does not directly solve this problem. However, it provides an alternative approach that can be used in conjunction with other solutions.
Bitcoin Blockchain Solution
A Bitcoin block is essentially a group of transactions linked together and verified by a network of computers called miners. These nodes work together to verify the transactions and create a new block. One way to think of this process as a BGP solution is through the concept of “consensus.”
In the context of blockchain, consensus refers to an agreement among nodes about the collective state of the network. For example, when multiple nodes in a graph agree on a value (e.g., a timestamp), it means that all nodes have reached a common understanding. This consensus process is not directly related to the BGP solution, but rather serves as a mechanism to ensure that nodes maintain a shared view of the state of the blockchain.
Ethereum’s Approach
Built on a proof-of-work (PoW) consensus algorithm, Ethereum provides an alternative approach to the BGP solution. One way to solve the problem is to use a “decentralized ordering,” which involves aggregating multiple data sources to create a single authoritative ordering.
In Ethereum, nodes can participate in the network and contribute their local ordering information (e.g., transaction timestamps) to achieve a shared view of the state of the blockchain. This allows nodes to agree on the collective state of the network without relying solely on central authorities or consensus mechanisms like Bitcoin.
Example: Ethereum’s Byzantine General Solution
To illustrate how Ethereum solves BGP, consider the following scenario:
Imagine two nodes, node A and node B, connected in a graph. Each node has its own set of local ordering information (e.g., transaction timestamps) for a particular block of transactions. The goal is to determine whether it is possible for at most two nodes to agree on the collective state of the network.
Node A knows that all transactions in this block have been verified by node B and are therefore “valid”. However, node B does not need to know anything about other blocks or transactions beyond its local ordering information. In this case, Node A can use Ethereum’s decentralized ordering to aggregate multiple data sources (e.g., node timestamps) and create a single authoritative ordering.
In this way, node A can determine whether at most two nodes agree on the collective state of the network, thereby solving the general Byzantine problem for that particular block. This approach provides an alternative solution to the BGP problem that is more resistant to Byzantine attacks.
Conclusion
In conclusion, while the Bitcoin blockchain solves some of the problems associated with the general Byzantine problem, the main Ethereum blockchain does not directly solve this problem. However, Ethereum’s decentralized ordering approach can be used in conjunction with other solutions to provide an alternative method of solving the BGP problem.