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.[3]:ch. 5


When you pay someone in bitcoin, you set in motion a process of escalating, energy-intensive complexity. Your payment is basically an electronic message, which contains the complete lineage of your bitcoin, along with data about who you’re sending it to (and, if you choose, a small processing fee). That message gets converted by encryption software into a long string of letters and numbers, which is then broadcast to every miner on the bitcoin network (there are tens of thousands of them, all over the world). Each miner then gathers your encrypted payment message, along with any other payment messages on the network at the time (usually in batches of around 2,000), into what’s called a block. The miner then uses special software to authenticate each payment in the block—verifying, for example, that you owned the bitcoin you’re sending, and that you haven’t already sent that same bitcoin to someone else.
How hard are the puzzles involved in mining? Well, that depends on how much effort is being put into mining across the network. The difficulty of the mining can be adjusted, and is adjusted by the protocol every 2016 blocks, or roughly every 2 weeks. The difficulty adjusts itself with the aim of keeping the rate of block discovery constant. Thus if more computational power is employed in mining, then the difficulty will adjust upwards to make mining harder.  And if computational power is taken off of the network, the opposite happens. The difficulty adjusts downward to make mining easier.
In addition to being the means of generating new bitcoin, bitcoin mining creates the blockchain that verifies bitcoin transactions. The block reward is gleaned by placing a new block on the blockchain, which acts as an advancing public ledger of verified transaction. This is an essential function for bitcoin's operation as it enables the currency to be safely and predictably created without the centralized regulation in the form of a bank or federal government. Blocks must to be a validated by a proof-of-work (Bitcoin uses Hashcash), which can only be obtained by expending a great deal of processing power. Once a block is obtained a message is broadcast to the mining network and verified by all recipients. 
Transactions are verified by network nodes through cryptography and recorded in a public distributed ledger called a blockchain. Bitcoin was invented by an unknown person or group of people using the name Satoshi Nakamoto[9] and released as open-source software in 2009.[10] Bitcoins are created as a reward for a process known as mining. They can be exchanged for other currencies,[11] products, and services. Research produced by the University of Cambridge estimates that in 2017, there were 2.9 to 5.8 million unique users using a cryptocurrency wallet, most of them using bitcoin.[12]
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