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=== Introduction === Introduction
((("bitcoin","establishing ownership of")))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 de-centralized trust and control, ownership attestation, and the cryptographic-proof security model. ((("bitcoin","establishing ownership of")))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 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 block chain or access to the Internet. Keys enable many of the interesting properties of bitcoin, including de-centralized trust and control, ownership attestation, and the cryptographic-proof security model.
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) key and a public key. Think of the public key as similar to a bank account number and the private key as similar to the secret PIN, or signature on a check 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. Every bitcoin transaction requires a valid signature to be included in the block chain, 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) key and a public key. Think of the public key as similar to a bank account number and the private key as similar to the secret PIN, or signature on a check 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.
In the payment portion of a bitcoin transaction, the recipient's public key is represented by its digital fingerprint, called a((("addresses, bitcoin","defined"))) _bitcoin address_, which is used in the same way as the beneficiary name on a check (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 checks: 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, because this is the part they need to share with the world. In the payment portion of a bitcoin transaction, the recipient's public key is represented by its digital fingerprint, called a((("addresses, bitcoin","defined"))) _bitcoin address_, which is used in the same way as the beneficiary name on a check (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 checks: a single payment instrument that can be used to pay into people's accounts, pay into company accounts, pay for bills, or pay to cash. The bitcoin address is the only representation of the keys that users will routinely see, because 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 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. 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 Crypto-Currency ==== Public Key Cryptography and Cryptocurrency
((("keys", id="ix_ch04-asciidoc0", range="startofrange")))((("crypto-currency")))((("keys","crypto-currency and")))((("keys","public")))((("public key cryptography")))((("public key cryptography","implementation of")))Public key cryptography was invented in the 1970s and is a mathematical foundation for computer and information security. ((("keys", id="ix_ch04-asciidoc0", range="startofrange")))((("cryptocurrency")))((("keys","cryptocurrency and")))((("keys","public")))((("public key cryptography")))((("public key cryptography","implementation of")))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"))) 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. Since the invention of public key cryptography, several suitable mathematical functions, such as((("prime number exponentiation"))) 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.
@ -32,7 +32,7 @@ When spending bitcoins, the current bitcoin owner presents her public key and a
[[private_public_keys]] [[private_public_keys]]
==== Private and Public Keys ==== Private and Public Keys
((("keys","public/private")))((("keys","in wallets")))((("private keys")))((("public keys")))((("wallets","public/private keys in")))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 in <<k_to_K_to_A>>. ((("keys","public/private")))((("keys","in wallets")))((("private keys")))((("public keys")))((("wallets","public/private keys in")))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 in <<k_to_K_to_A>>.
[[k_to_K_to_A]] [[k_to_K_to_A]]
.Private key, public key, and bitcoin address .Private key, public key, and bitcoin address
@ -45,7 +45,7 @@ image::images/msbt_0401.png["privk_to_pubK_to_addressA"]
[TIP] [TIP]
==== ====
((("private keys","creating by hand")))The bitcoin private key is just a number. You can pick your private keys randomly using just a coin, pencil, and paper: toss a coin 256 times and you have the binary digits of a random private key you can use in a bitcoin wallet. The public key can be then generated from the private key. ((("private keys","creating by hand")))The bitcoin private key is just a number. You can pick your private keys randomly using just a coin, pencil, and paper: toss a coin 256 times and you have the binary digits of a random private key you can use in a bitcoin wallet. The public key can then be generated from the private key.
==== ====
===== Generating a private key from a random number ===== Generating a private key from a random number