For one, proof of work prevents miners from creating bitcoins out of thin air: they must burn real energy to earn them. And two, proof of work ossifies Bitcoin’s history. If an attacker were to try and change a transaction that happened in the past, that attacker would have to redo all of the work that has been done since to catch up and establish the longest chain. This is practically impossible and is why miners are said to “secure” the Bitcoin network.

Bitcoin is a cryptocurrency and worldwide payment system. It is the first decentralized digital currency, as the system works without a central bank or single administrator. The network is peer-to-peer and transactions take place between users directly, without an intermediary. These transactions are verified by network nodes through the use of cryptography and recorded in a public distributed ledger called a blockchain. Bitcoin was invented by an unknown person or group of people under the name Satoshi Nakamoto and released as open-source software in 2009.
Bitcoin mining is intentionally designed to be resource-intensive and difficult so that the number of blocks found each day by miners remains steady. Individual blocks must contain a proof of work to be considered valid. This proof of work is verified by other Bitcoin nodes each time they receive a block. Bitcoin uses the hashcash proof-of-work function.
^ Jump up to: a b c d Joshua A. Kroll; Ian C. Davey; Edward W. Felten (11–12 June 2013). "The Economics of Bitcoin Mining, or Bitcoin in the Presence of Adversaries" (PDF). The Twelfth Workshop on the Economics of Information Security (WEIS 2013). Archived (PDF) from the original on 9 May 2016. Retrieved 26 April 2016. A transaction fee is like a tip or gratuity left for the miner.
Transactions are defined using a Forth-like scripting language.[3]:ch. 5 Transactions consist of one or more inputs and one or more outputs. When a user sends bitcoins, the user designates each address and the amount of bitcoin being sent to that address in an output. To prevent double spending, each input must refer to a previous unspent output in the blockchain.[67] The use of multiple inputs corresponds to the use of multiple coins in a cash transaction. Since transactions can have multiple outputs, users can send bitcoins to multiple recipients in one transaction. As in a cash transaction, the sum of inputs (coins used to pay) can exceed the intended sum of payments. In such a case, an additional output is used, returning the change back to the payer.[67] Any input satoshis not accounted for in the transaction outputs become the transaction fee.[67]
In 2014 prices started at $770 and fell to $314 for the year.[31] In February 2014 the Mt. Gox exchange, the largest bitcoin exchange at the time, said that 850,000 bitcoins had been stolen from its customers, amounting to almost $500 million. Bitcoin's price fell by almost half, from $867 to $439 (a 49% drop). Prices remained low until late 2016.[citation needed]
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