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Bitcoin uses public-key cryptography, in which a pair of a public and a private cryptographic key is generated. A collection of keys is called a wallet. Note that sometimes the term is used to mean the software in the sense of digital wallet. A Bitcoin transaction transfers ownership to a new address, a string having the form of random letters and numbers derived from public keys by application of a hash function and encoding scheme.The corresponding private keys act as a safeguard for the owner; a valid payment message from an address must contain the associated public key and a digital signature proving possession of the associated private key. Theft of bitcoins has occurred on numerous occasions, and the practical day-to-day security of Bitcoin wallets is a concern like the security of other forms of payment.

Risk of theft can be reduced by generating keys offline on anuncompromised computer and saving them on external storage or paper printouts. “Physical bitcoins”, ubiquitous in media coverage of Bitcoin, are produced by various vendors. They store a private key on paper, metal, wood, or plastic. There are also digital products known as “Hardware Wallets” to store bitcoins securely on a physical device. Bitcoins can be lost. In 2013 one user said he lost 7,500 bitcoins, worth $7.5m at the time, when he discarded a hard drive containing his private key. Bitcoins can be found; In March 2014, former Bitcoin exchange Mt. Gox reported it found an “old wallet, which was used before June 2011, [that] held about 200,000 Bitcoins”.

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Software
Bitcoin wallet software, sometimes called a Bitcoin client software, allows a user to transact bitcoins. A wallet program generates and stores private keys, and communicates with peers on the Bitcoin network. The first wallet program called Bitcoin-Qt was released in 2009 by Satoshi Nakamoto asopen source code. It can be used as a desktop wallet for payments or as a server utility for merchants and other payment services. Bitcoin-Qt, also called “Satoshi client” is sometimes referred to as the reference client because it serves to define the Bitcoin protocol and acts as a standard for other implementations. As of version 0.9, Bitcoin-QT has been renamed “Bitcoin Core” to more accurately describe its role in the network.When making a purchase with a mobile device, QR codes are used ubiquitously to simplify transactions. Several server software implementations of the Bitcoin protocol exist. So-called “full” nodes on the network validate transactions and blocks they receive, and relay them to connected peers

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