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How Does “Proof-of-Work” Secure a Blockchain?

Proof-of-Work (PoW) secures a blockchain by requiring miners to expend significant computational effort (hash power) to solve a complex mathematical problem to create a new block. This effort makes it prohibitively expensive and energy-intensive for a malicious actor to gain control of the network (the 51% attack).

The longest chain of blocks is accepted as the valid history.

What Is the Role of a ‘Nakamoto Consensus’ in Resolving Chain Splits?
Why Is Proof of Work Considered Secure?
How Does a Proof-of-Work (PoW) Consensus Mechanism Prevent Double-Spending?
What Is a 51 Percent Attack and How Does It Exploit the Longest Chain Rule?