Unauthorized spending is mitigated by bitcoin's implementation of public-private key cryptography. For example; when Alice sends a bitcoin to Bob, Bob becomes the new owner of the bitcoin. Eve observing the transaction might want to spend the bitcoin Bob just received, but she cannot sign the transaction without the knowledge of Bob's private key.
If the random number generator is not random enough, that means someone else can recreate the private key of the hardware wallet easier. This attack has happened in the past with blockchain.info, a web wallet. Over 300 BTC were lost because blockchain.info did not use good RNG, so a hacker was able to generate the private keys again and steal coins.
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The incremental complexity and technological know-how needed for this method are both downsides to the paper wallet approach. Cold storage solutions and hardware wallets are less nimble than other options, too; if the price of bitcoin were crashing, for example, you might find yourself slower to the draw than if you merely kept your BTC on a site like Coinbase.
As noted in Nakamoto's whitepaper, it is possible to verify bitcoin payments without running a full network node (simplified payment verification, SPV). A user only needs a copy of the block headers of the longest chain, which are available by querying network nodes until it is apparent that the longest chain has been obtained. Then, get the Merkle branch linking the transaction to its block. Linking the transaction to a place in the chain demonstrates that a network node has accepted it, and blocks added after it further establish the confirmation.
Bitcoin mining is the process of updating the ledger of Bitcoin transactions known as the blockchain. Mining is done by running extremely powerful computers (known as ASICs) that race against other miners in an attempt to guess a specific number. The first miner to guess the number gets to update the ledger of transactions and also receives a reward of newly minted Bitcoins (currently the reward is 12.5 Bitcoins).
A specific problem that an internet payment system must solve is double-spending, whereby a user pays the same coin to two or more different recipients. An example of such a problem would be if Eve sent a bitcoin to Alice and later sent the same bitcoin to Bob. The bitcoin network guards against double-spending by recording all bitcoin transfers in a ledger (the blockchain) that is visible to all users, and ensuring for all transferred bitcoins that they haven't been previously spent.:4
Bitcoin prices were negatively affected by several hacks or thefts from cryptocurrency exchanges, including thefts from Coincheck in January 2018, Coinrail and Bithumb in June, and Bancor in July. For the first six months of 2018, $761 million worth of cryptocurrencies was reported stolen from exchanges. Bitcoin's price was affected even though other cryptocurrencies were stolen at Coinrail and Bancor, as investors worried about the security of cryptocurrency exchanges.