Because of bitcoin's decentralized nature and its trading on online exchanges located in many countries, regulation of bitcoin has been difficult. However, the use of bitcoin can be criminalized, and shutting down exchanges and the peer-to-peer economy in a given country would constitute a de facto ban.[176] The legal status of bitcoin varies substantially from country to country and is still undefined or changing in many of them. Regulations and bans that apply to bitcoin probably extend to similar cryptocurrency systems.[177]
In the blockchain, bitcoins are registered to bitcoin addresses. Creating a bitcoin address requires nothing more than picking a random valid private key and computing the corresponding bitcoin address. This computation can be done in a split second. But the reverse, computing the private key of a given bitcoin address, is mathematically unfeasible. Users can tell others or make public a bitcoin address without compromising its corresponding private key. Moreover, the number of valid private keys is so vast that it is extremely unlikely someone will compute a key-pair that is already in use and has funds. The vast number of valid private keys makes it unfeasible that brute force could be used to compromise a private key. To be able to spend their bitcoins, the owner must know the corresponding private key and digitally sign the transaction. The network verifies the signature using the public key; the private key is never revealed.[7]:ch. 5
Transactions that occur through the use and exchange of these altcoins are independent from formal banking systems, and therefore can make tax evasion simpler for individuals. Since charting taxable income is based upon what a recipient reports to the revenue service, it becomes extremely difficult to account for transactions made using existing cryptocurrencies, a mode of exchange that is complex and difficult to track.[66]
You don‘t need to understand the details about SHA 256. It‘s only important you know that it can be the basis of a cryptologic puzzle the miners compete to solve. After finding a solution, a miner can build a block and add it to the blockchain. As an incentive, he has the right to add a so-called coinbase transaction that gives him a specific number of Bitcoins. This is the only way to create valid Bitcoins.

Though each bitcoin transaction is recorded in a public log, names of buyers and sellers are never revealed – only their wallet IDs. While that keeps bitcoin users’ transactions private, it also lets them buy or sell anything without easily tracing it back to them. That’s why it has become the currency of choice for people online buying drugs or other illicit activities.
Blockchain analysts estimate that Nakamoto had mined about one million bitcoins[32] before disappearing in 2010, when he handed the network alert key and control of the code repository over to Gavin Andresen. Andresen later became lead developer at the Bitcoin Foundation.[33][34] Andresen then sought to decentralize control. This left opportunity for controversy to develop over the future development path of bitcoin, in contrast to the perceived authority of Nakamoto's contributions.[35][34]
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