1. Introduction
In this post we analyze two sources of divergence on the blockchain caused respectively by a natural fork and a malicious fork. The revolution that has been brought about by Bitcoin’s blockchain is a direct result of its open nature. Indeed, anyone can be part of it, suggest changes to it, mine new blocks in it, or simply conduct routine validations on it. It is in many respects, the epitome of decentralization and censorship-resistance. Its appealing nature is in large part rooted in its rich interdisciplinary foundation that spans across philosophy, mathematics and economics.
But beyond the elegance of its theoretical underpinning, the blockchain’s seamless implementation rests on an inherent agreement between its different participants. Without agreement, this harmonious apparatus would likely decay into chaos. The rather flawless operation of the system is the result of a particular consensus protocol known as Proof of Work (or PoW for short).
The consensus is meant to be amongst all of the miners on the network. It stipulates that any miner always extend the chain of blocks with the highest amount of cumulative work. In this context, work is a measure of the expected computational effort that a miner exerts in order to solve a given cryptographic challenge. In essence, the challenge consists in finding a value that makes the computation emit an output with a mandatory minimum number 
of leading 0’s. The work associated with mining a given block corresponds to the value 
where is dynamically adjusted to ensure that the network’s average block rate remains constant at 
0.00167 blocks / second (i.e., 1 block per 10 minutes). We discuss PoW as well as other consensus protocols in more details in another post.
In an ideal setting where all miners are honest (i.e., abide by the PoW consensus protocol) and where blocks are propagated instantaneously on the network, all the nodes will always have a unified view of the blockchain — barring the extremely unlikely scenario of two distinct miners generating two valid blocks at the exact same time). However, imperfections do exist:
- Imperfection #1: The network incurs an information propagation delay. As a result, every new block takes a positive amount of time to reach all the other nodes on the network.
- Imperfection #2: There exists a subset of dishonest miners that decide to disregard the PoW consensus protocol. As a result, such miners can fork the blokchain and start mining on top of a parallel chain different than the one with the highest amount of cumulative work.