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instrument that can be used to pay into people’s accounts, company accounts, pay for bills or pay to cash. The bitcoin address is the only representation of the keys that users will routinely see, as this is the part they need to share with the world. In this chapter we will introduce wallets, which contain cryptographic keys. We will look at how keys are generated, stored and managed. We will review the various en‐ coding formats used to represent private and public keys, addresses and script addresses. Finally we will look at special uses of keys: to sign messages, to prove ownership and to create vanity addresses and paper wallets. Public key cryptography and crypto-currency Public key cryptography was invented in the 1970s and is a mathematical foundation for computer and information security. Since the invention of public key cryptography, several suitable mathematical functions, such as prime number exponentiation and elliptic curve multiplication, have been dis‐ covered. These mathematical functions are practically irreversible, meaning that they are easy to calculate in one direction and infeasible to calculate in the opposite direction. Based on these mathematical functions, cryptography enables the creation of digital secrets and unforgeable digital signatures. Bitcoin uses elliptic curve multiplication as the basis for its public key cryptography. In bitcoin, we use public key cryptography to create a key pair that controls access to bitcoins. The key pair consists of a private key and — derived from it — a unique public key. The public key is used to receive bitcoins, and the private key is used to sign trans‐ actions to spend those bitcoins. There is a mathematical relationship between the public and the private key that allows the private key to be used to generate signatures on messages. This signature can be validated against the public key without revealing the private key. When spending bitcoins, the current bitcoin owner presents their public key and a signature (different each time, but created from the same private key; see (to come)) in a transaction to spend those bitcoins. Through the presentation of the public key and signature everyone in the bitcoin network can verify and accept the transaction as valid, confirming that the person transferring the bitcoins owned them at the time of the transfer. In most wallet implementations, the private and public keys are stor‐ ed together as a key pair for convenience. However, the public key can be calculated from the private key, so storing only the private key is also possible. 62 | Chapter 4: Keys, Addresses, WalletsPDF Image | Mastering Bitcoin
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