Ownership of Bitcoin
Ownership of bitcoin is established through digital keys, bitcoin addresses, and digital signatures. The digital keys are not actually stored in the network but are instead created and stored by end-users in a file or simple database called a wallet. The digital keys in a user’s wallet are completely independent of the bitcoin protocol and can be generated and managed by the user’s wallet software without reference to the blockchain or access to the Internet. Keys enable many of the interesting properties of bitcoin, including decentralized trust and control, ownership attestation, and the cryptographic-proof security model.
Bitcoin Transaction and Key Control
Every bitcoin transaction requires a valid signature to be included in the blockchain, which can only be generated with valid digital keys. Therefore, anyone with a copy of those keys has control of the bitcoin in that account. Keys come in pairs consisting of a private (secret) and public key. Think of the public key as similar to a bank account number and the private key as similar to the secret PIN number or signature on a cheque that provides control over the account. These digital keys are very rarely seen by the users of bitcoin. For the most part, they are stored inside the wallet file and managed by the bitcoin wallet software.
Bitcoin Address Representation
In the payment portion of a bitcoin transaction, the recipient’s public key is represented by its digital fingerprint, called a bitcoin address, which is used in the same way as the beneficiary name on a cheque (i.e., “Pay to the order of”). In most cases, a bitcoin address is generated from and corresponds to a public key. However, not all bitcoin addresses represent public keys; they can also represent other beneficiaries such as scripts, as we will see later in this chapter. This way, bitcoin addresses abstract the recipient of funds, making transaction destinations flexible, similar to paper cheques: a single payment 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.
Introduction to Wallets and Keys
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 encoding 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 Cryptocurrency
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 discovered. 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.
Key Pair and Bitcoin Transactions
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 transactions 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.
Information about Bitcoin Core
Bitcoin Ownership Verification
When spending bitcoins, the current bitcoin owner presents their public key and a signature (different each time but created from the same private key) 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.
Private and Public Keys
A bitcoin wallet contains a collection of key pairs, each consisting of a private key and a public key. The private key (k) is a number, usually picked at random. From the private key, we use elliptic curve multiplication, a one-way cryptographic function, to generate a public key (K). From the public key (K), we use a one-way cryptographic hash function to generate a bitcoin address (A). In this section, we will start with generating the private key, look at the elliptic curve math that is used to turn that into a public key, and finally, generate a bitcoin address from the public key. The relationship between private key, public key, and bitcoin address is shown below:
Private Keys
A private key is simply a number, picked at random. Ownership and control over the private key is the root of user control over all funds associated with the corresponding bitcoin address. The private key is used to create signatures that are required to spend bitcoins by proving ownership of funds used in a transaction. The private key must remain secret at all times, as revealing it to a third party is equivalent to giving them control over the bitcoins secured by that key. The private key must also be backed up and protected from accidental loss since if lost, it cannot be recovered and the funds secured by it are forever lost too.
