A 51% attack occurs when a single entity gains majority control of a blockchain's consensus mechanism, over 50% of hash power in Proof of Work or over 50% of stake in Proof of Stake, enabling them to manipulate the blockchain's canonical history. With majority control, the attacker can build blocks faster than the honest network, eventually producing a longer chain that replaces the legitimate one. This enables double-spending: spend coins on the honest chain, then publish an alternate chain where those coins were never spent, effectively using them twice. Attackers can also exclude specific transactions (censorship), reorder transactions for profit (MEV extraction), and prevent other miners from earning rewards. What attackers cannot do: create coins from nothing, steal coins from addresses they don't control, or change protocol rules that nodes enforce. The attack is economically bounded: acquiring 51% of Bitcoin's hash power would cost billions in hardware and electricity, and acquiring 51% of Ethereum's stake would require tens of billions of dollars while destroying the value of the stake itself. Small-cap chains with limited hash power or stake have been successfully attacked, Ethereum Classic, Bitcoin Gold, and others suffered double-spend attacks. The economic security model assumes attack cost exceeds attack profit. For major chains, this holds convincingly; for small chains, the math is less favorable.
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