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=== Introduction
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.
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.
The digital keys within each user's wallet allow the user to sign transactions, thereby providing cryptographic proof of the ownership of the bitcoins sourced by the transaction. 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.
@ -18,11 +18,11 @@ In this chapter we will introduce wallets, which contain cryptographic keys. We
((("public key")))
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.
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.
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. These signatures can then be checked against the public key to verify ownership, without the bitcoin owner revealing their private key at any stage during the process.
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 <<signature>>) 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.
@ -142,7 +142,7 @@ image::images/ecc-over-F17-math.png["ecc-over-F17-math"]
[[public_key_derivation]]
==== Generating a public key
Starting with a private key in the form of a randomly generated number +k+, we multiply by a predetermined point on the curve called the _generator point_ +G+ to produce another point somewhere else on the curve, which is the corresponding public key +K+. The generator point is specified as part of the +secp256k1+ standard and is always the same for all keys in bitcoin.
Starting with a private key in the form of a randomly generated number +k+, we multiply it by a predetermined point on the curve called the _generator point_ +G+ to produce another point somewhere else on the curve, which is the corresponding public key +K+. The generator point is specified as part of the +secp256k1+ standard and is always the same for all keys in bitcoin.
[latexmath]
++++
@ -188,9 +188,9 @@ A private key can be converted into a public key, but a public key cannot be con
An address is a string of digits and characters that can be shared with anyone who wants to send you money. In bitcoin, addresses produced from public keys begin with the digit "1". The bitcoin address is what appears most commonly in a transaction as the "recipient" of the funds. If we were to compare a bitcoin transaction to a paper cheque, the bitcoin address is the beneficiary, which is what we write on the line after "Pay to the order of". On a paper cheque, that beneficiary can sometimes be the name of a bank account holder, but can also include corporations, institutions or even cash. Because paper cheques do not need to specify an account, but rather use an abstract name as the recipient of funds, that makes paper cheques very flexible as payment instruments. Bitcoin transactions use a similar abstraction, the bitcoin address, to make them very flexible. A bitcoin address can represent the owner of a private/public key pair, or it can represent something else, such as a payment script, as we will see in <<p2sh>>. For now, let's examine the simple case, a bitcoin address that represents, and is derived from, a public key.
A bitcoin address derived from a public key is a string of numbers and letters that begins with the number one, such as +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy+. A bitcoin address is generated from the public key through the use of one-way cryptographic hashing; a "hashing algorithm" or simply "hash algorithm" is a one-way function that produces a fingerprint or "hash" of an arbitrary sized input. Cryptographic hash functions are used extensively in bitcoin: in bitcoin addresses, script addresses and in the mining "Proof-of-Work" algorithm. The algorithms used to make a bitcoin address from a public key are the Secure Hash Algorithm (SHA) and the RACE Integrity Primitives Evaluation Message Digest (RIPEMD), specifically SHA256 and RIPEMD160.
A bitcoin address derived from a public key is a string of numbers and letters that begins with the number one, such as +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy+. The bitcoin address is derived from the public key through the use of one-way cryptographic hashing; a "hashing algorithm" or simply "hash algorithm" is a one-way function that produces a fingerprint or "hash" of an arbitrary sized input. Cryptographic hash functions are used extensively in bitcoin: in bitcoin addresses, script addresses and in the mining "Proof-of-Work" algorithm. The algorithms used to make a bitcoin address from a public key are the Secure Hash Algorithm (SHA) and the RACE Integrity Primitives Evaluation Message Digest (RIPEMD), specifically SHA256 and RIPEMD160.
Starting with the public key K, we compute the SHA256 hash, and then compute the RIPEMD160 hash of the result, producing a 160 bit (20 byte) number:
Starting with the public key K, we compute the SHA256 hash and then compute the RIPEMD160 hash of the result, producing a 160 bit (20 byte) number:
[latexmath]
++++
\begin{equation}
@ -199,7 +199,7 @@ Starting with the public key K, we compute the SHA256 hash, and then compute the
++++
where K is the public key and A is the resulting bitcoin address.
Bitcoin addresses are almost always presented to users in an encoding called "Base58Check" (see <<base58check>> below), which uses 58 characters (a base-58 number system) and a checksum to help human readability, avoid ambiguity, and protect against errors in address transcription and entry. Base58Check is also used in many other ways in bitcoin, whenever there is a need for a user to read and correctly transcribe a number, such as a bitcoin address, a private key, an encrypted key, or a script hash. In the next section we will examine the mechanics of Base58Check encoding and decoding, and the resulting representations.
Bitcoin addresses are almost always presented to users in an encoding called "Base58Check" (see <<base58check>> below), which uses 58 characters (a base-58 number system) and a checksum to help human readability, avoid ambiguity and protect against errors in address transcription and entry. Base58Check is also used in many other ways in bitcoin, whenever there is a need for a user to read and correctly transcribe a number, such as a bitcoin address, a private key, an encrypted key, or a script hash. In the next section we will examine the mechanics of Base58Check encoding and decoding, and the resulting representations.
[[pubkey_to_adddress]]
.Public Key to Bitcoin Address: Conversion of a public key into a bitcoin address
@ -221,7 +221,7 @@ In order to represent long numbers in a compact way, using fewer symbols, many c
[[base58check]]
===== Base58Check Encoding
To add extra security against typos or transcription errors, Base58Check has a built-in error-checking code. The checksum is an additional four bytes added to the end of the data that is being encoded. The checksum is derived from the hash of the encoded data and can therefore be used to detect and prevent transcription and typing errors. When presented with a Base58Check code, the decoding software will calculate the checksum of the data and compare it to the checksum included in the code. If the two do not match, that indicates that an error has been introduced and the Base58Check data is invalid. For example, this prevents a mistyped bitcoin address from being accepted by the wallet software as a valid destination, an error which would otherwise result in loss of funds.
To add extra security against typos or transcription errors, Base58Check is a Base-58 encoding format, frequently used in bitcoin, which has a built-in error-checking code. The checksum is an additional four bytes added to the end of the data that is being encoded. The checksum is derived from the hash of the encoded data and can therefore be used to detect and prevent transcription and typing errors. When presented with a Base58Check code, the decoding software will calculate the checksum of the data and compare it to the checksum included in the code. If the two do not match, that indicates that an error has been introduced and the Base58Check data is invalid. For example, this prevents a mistyped bitcoin address from being accepted by the wallet software as a valid destination, an error which would otherwise result in loss of funds.
To convert data (a number) into a Base58Check format, we first add a prefix to the data, called the "version byte", which serves to easily identify the type of data that is encoded. For example, in the case of a bitcoin address the prefix is zero (0x00 in hex), whereas the prefix used when encoding a private key is 128 (0x80 in hex). A list of common version prefixes is shown below in <<base58check_versions>>.
@ -470,11 +470,11 @@ Private keys must remain secret. The need for _confidentiality_ of the private k
BIP0038 proposes a common standard for encrypting private keys with a passphrase and encoding them with Base58Check so that they can be stored securely on backup media, transported securely between wallets or in any other conditions where the key might be exposed. The standard for encryption uses the Advanced Encryption Standard (AES), a standard established by the National Institute of Standards and Technology (NIST) and used broadly in data encryption implementations for commercial and military applications.
A BIP0038 encryption scheme takes a bitcoin private key, usually encoded in the Wallet Import Format (WIF), as a Base58Check string with a prefix of "5".
Additionally, the BIP0038 encryption scheme takes a passphrase -- a long password -- usually composed of several words or a complex string of alphanumeric characters. The result of the BIP0038 encryption scheme is a Base58Check encoded encrypted private key that begins with the prefix +6P+. If you see a key that starts with +6P+ that means it is encrypted and requires a passphrase in order to convert (decrypt) it back into a WIF-formatted private key (prefix +5+) that can be used in any wallet. Many wallet applications now recognize BIP0038 encrypted private keys and will prompt the user for a passphrase to decrypt and import the key. Third party applications, such as the incredibly useful browser-based https://bitaddress.org (Wallet Details tab), can be used to decrypt BIP0038 keys.
Additionally, the BIP0038 encryption scheme takes a passphrase -- a long password -- usually composed of several words or a complex string of alphanumeric characters. The result of the BIP0038 encryption scheme is a Base58Check encoded encrypted private key that begins with the prefix +6P+. If you see a key that starts with +6P+ that means it is encrypted and requires a passphrase in order to convert (decrypt) it back into a WIF-formatted private key (prefix +5+) that can be used in any wallet. Many wallet applications now recognize BIP0038 encrypted private keys and will prompt the user for a passphrase to decrypt and import the key. Third party applications, such as the incredibly useful browser-based bitaddress.org (Wallet Details tab), can be used to decrypt BIP0038 keys.
The most common use case for BIP0038 encrypted keys is for paper wallets that can be used to backup private keys on a piece of paper. As long as the user selects a strong passphrase, a paper wallet with BIP0038 encrypted private keys is incredibly secure and a great way to create offline bitcoin storage (also known as "cold storage")
Test the following encrypted keys using https://bitaddress.org to see how you can get the decrypted key by entering the passphrase:
Test the following encrypted keys using bitaddress.org to see how you can get the decrypted key by entering the passphrase:
.Example of BIP0038 Encrypted Private Key
|=======
@ -551,7 +551,7 @@ Let's look at the pattern "1Kids" as a number and see how frequently we might fi
As you can see, Eugenio won't be creating the vanity address "1KidsCharity" any time soon, even if he had access to several thousand computers. Each additional character increases the difficulty by a factor of 58. Patterns with more than seven characters are usually found by specialized hardware, such as custom-built desktops with multiple Graphical Processing Units (GPUs). These are often re-purposed bitcoin mining "rigs" that are no longer profitable for bitcoin mining but can be used effectively to find vanity addresses. Vanity searches on GPU systems are many orders of magnitude faster than on a general-purpose CPU.
Another way to find a vanity address is to outsource the work to a pool of vanity-miners, such as the pool at https://vanitypool.appspot.com. A pool is a service that allows those with GPU hardware to earn bitcoin searching for vanity addresses for others. For a small payment (0.01 bitcoin or approximately $5 when this was written), Eugenio can outsource the search for a 7-character pattern vanity address and get results in a few hours instead of having to run a CPU search for months.
Another way to find a vanity address is to outsource the work to a pool of vanity-miners, such as the pool at vanitypool.appspot.com. A pool is a service that allows those with GPU hardware to earn bitcoin searching for vanity addresses for others. For a small payment (0.01 bitcoin or approximately $5 when this was written), Eugenio can outsource the search for a 7-character pattern vanity address and get results in a few hours instead of having to run a CPU search for months.
===== Vanity Address Security
@ -584,14 +584,14 @@ Paper wallets come in many shapes, sizes and designs, but at a very basic level
| Private Key (WIF) | 5J3mBbAH58CpQ3Y5RNJpUKPE62SQ5tfcvU2JpbnkeyhfsYB1Jcn
|=======
Paper wallets can be generated easily using a tool such as the client-side Javascript generator at https://bitaddress.org. This page contains all the code necessary to generate keys and paper wallets, even while completely disconnected from the Internet. To use it, save the HTML page on your local drive or on an external USB flash drive. Disconnect from the Internet and open the file in a browser. Even better, boot your computer using a pristine operating system, such as a CDROM bootable Linux OS. Any keys generated with this tool while offline can be printed on a local printer over a USB cable (not wirelessly), thereby creating paper wallets whose keys exist only on the paper and have never been stored on any online system. Put these paper wallets in a fire-proof safe and "send" bitcoin to their private address, to implement a simple yet highly effective "cold storage" solution.
Paper wallets can be generated easily using a tool such as the client-side Javascript generator at bitaddress.org. This page contains all the code necessary to generate keys and paper wallets, even while completely disconnected from the Internet. To use it, save the HTML page on your local drive or on an external USB flash drive. Disconnect from the Internet and open the file in a browser. Even better, boot your computer using a pristine operating system, such as a CDROM bootable Linux OS. Any keys generated with this tool while offline can be printed on a local printer over a USB cable (not wirelessly), thereby creating paper wallets whose keys exist only on the paper and have never been stored on any online system. Put these paper wallets in a fire-proof safe and "send" bitcoin to their private address, to implement a simple yet highly effective "cold storage" solution.
.An example of a simple paper wallet from https://bitaddress.org
.An example of a simple paper wallet from bitaddress.org
image::images/paper_wallet_simple.png["paper_wallet_simple"]
The disadvantage of the simple paper wallet system is that the printed keys are vulnerable to theft. A thief who is able to gain access to the paper can either steal it or photograph the keys and take control of the bitcoins locked with those keys. A more sophisticate paper wallet storage system uses BIP0038 encrypted private keys. The keys printed on the paper wallet are protected by a passphrase that the owner has memorized. Without the passphrase, the encrypted keys are useless. Yet, they still are superior to a passphrase protected wallet because the keys have never been online and must be physically retrieved from a safe or other physically secured storage.
.An example of an encrypted paper wallet from https://bitaddress.org. The passphrase is "test"
.An example of an encrypted paper wallet from bitaddress.org. The passphrase is "test"
image::images/paper_wallet_encrypted.png["paper_wallet_encrypted"]
[WARNING]
@ -601,10 +601,10 @@ While you can deposit funds into a paper wallet several times, you should withdr
Paper wallets come in many designs and sizes, with many different features. Some are intended to be given as gifts and have seasonal themes, such as Christmas and New Year's themes. Others are designed for storage in a bank vault or safe with the private key hidden in some way, either with opaque scratch-off stickers, or folded and sealed with tamper-proof adhesive foil.
.An example of a paper wallet from https://bitcoinpaperwallet.com with the private key on a folding flap.
.An example of a paper wallet from bitcoinpaperwallet.com with the private key on a folding flap.
image::images/paper_wallet_bpw.png["paper_wallet_bpw"]
.The https://bitcoinpaperwallet.com paper wallet with the private key concealed.
.The bitcoinpaperwallet.com paper wallet with the private key concealed.
image::images/paper_wallet_bpw_folded.jpg["paper_wallet_bpw_folded"]
Other designs feature additional copies of the key and address, in the form of detachable stubs similar to ticket stubs, allowing you to store multiple copies to protect against fire, flood or other natural disasters.