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.:ch. 5
As more and more miners competed for the limited supply of blocks, individuals found that they were working for months without finding a block and receiving any reward for their mining efforts. This made mining something of a gamble. To address the variance in their income miners started organizing themselves into pools so that they could share rewards more evenly. See Pooled mining and Comparison of mining pools.
Several news outlets have asserted that the popularity of bitcoins hinges on the ability to use them to purchase illegal goods. In 2014, researchers at the University of Kentucky found "robust evidence that computer programming enthusiasts and illegal activity drive interest in bitcoin, and find limited or no support for political and investment motives."
Bitcoin solves the "double spending problem" of electronic currencies (in which digital assets can easily be copied and re-used) through an ingenious combination of cryptography and economic incentives. In electronic fiat currencies, this function is fulfilled by banks, which gives them control over the traditional system. With bitcoin, the integrity of the transactions is maintained by a distributed and open network, owned by no-one.
In January 2009, the bitcoin network was created when Nakamoto mined the first block of the chain, known as the genesis block. Embedded in the coinbase of this block was the following text: "The Times 03/Jan/2009 Chancellor on brink of second bailout for banks." This note has been interpreted as both a timestamp and a comment on the instability caused by fractional-reserve banking.:18