Keys come in pairs. The public key is used to encrypt the message whereas the private key decrypts the message. The only person with the private key is you. Everyone else is free to have your public key. As a result, everyone can send you encrypted messages without having to agree on a key beforehand. They simply use your public key and you untangle the gibberish by using your private key.
Because it's similar to gold mining in that the bitcoins exist in the protocol's design (just as the gold exists underground), but they haven't been brought out into the light yet (just as the gold hasn't yet been dug up). The bitcoin protocol stipulates that 21 million bitcoins will exist at some point. What "miners" do is bring them out into the light, a few at a time.

Let your computer earn you money with Bitcoin Miner, the free easy-to-use Bitcoin miner! Earn Bitcoin which can be exchanged for real-world currency! Works great at home, work, or on the go. Download Bitcoin Miner and start mining Bitcoin today! Bitcoin miners perform complex calculations known as hashes. Each hash has a chance of yielding bitcoins. The more hashes performed, the more chances of earning bitcoins. Most people join a mining pool to increase their chances of earning bitcoins. Mining pools pay for high value hashes known as shares. The default mining pool issues payouts weekly to accounts with at least 5000 Satoshis. If an account doesn't reach 5000 Satoshis during a week, the balance carries forward (it is never lost).
The other two BitFury mines are in Tbilisi, in the Republic of Georgia, where the weather is much warmer. According to Vavilov, the company has developed a two-phase immersion cooling technology with their subsidiary, Allied Control. The system bathes the mining machines in a dielectric heat-transfer liquid called Novec, which cools the computers as it evaporates. The system is now deployed at the Georgia data centers.
As more miners join, the rate of block creation increases. As the rate of block generation increases, the difficulty rises to compensate, which has a balancing of effect due to reducing the rate of block-creation. Any blocks released by malicious miners that do not meet the required difficulty target will simply be rejected by the other participants in the network.

The domain name "bitcoin.org" was registered on 18 August 2008.[15] In November 2008, a link to a paper authored by Satoshi Nakamoto titled Bitcoin: A Peer-to-Peer Electronic Cash System[5] was posted to a cryptography mailing list. Nakamoto implemented the bitcoin software as open source code and released it in January 2009.[16][17][10] Nakamoto's identity remains unknown.[9]
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