((("cryptography", "defined")))((("cryptography", see="also keys and addresses")))You may have heard that bitcoin is based on _cryptography_, which is a branch of mathematics used extensively in computer security. Cryptography means "secret writing" in Greek, but the science of cryptography encompasses more than just secret writing, which is referred to as encryption. Cryptography can also be used to prove knowledge of a secret without revealing that secret (digital signature), or prove the authenticity of data (digital fingerprint). These types of cryptographic proofs are the mathematical tools critical to bitcoin and used extensively in bitcoin applications. ((("encryption")))((("encryption", see="also keys and addresses")))Ironically, encryption is not an important part of bitcoin, as its communications and transaction data are not encrypted and do not need to be encrypted to protect the funds. In this chapter we will introduce some of the cryptography used in bitcoin to control ownership of funds, in the form of keys, addresses, and wallets.
((("cryptography", "defined")))((("cryptography", see="also keys and addresses")))You may have heard that bitcoin is based on _cryptography_, which is a branch of mathematics used extensively in computer security. Cryptography means "secret writing" in Greek, but the science of cryptography encompasses more than just secret writing, which is referred to as encryption. Cryptography can also be used to prove knowledge of a secret without revealing that secret (digital signature), or prove the authenticity of data (digital fingerprint). These types of cryptographic proofs are the mathematical tools critical to bitcoin and used extensively in bitcoin applications. ((("encryption")))((("encryption", see="also keys and addresses")))Ironically, encryption is not an important part of bitcoin, as its communications and transaction data are not encrypted and do not need to be encrypted to protect the funds. In this chapter we will introduce some of the cryptography used in bitcoin to control ownership of funds, in the form of keys, addresses, and wallets.
=== Introduction
((("digital keys", see="keys and addresses")))((("keys and addresses", "overview of", id="KAover04")))((("digital signatures", "purpose 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 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.
((("digital keys", see="keys and addresses")))((("keys and addresses", "overview of", id="KAover04")))((("digital signatures", "purpose 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 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.
Most bitcoin transactions require a valid digital signature to be included in the blockchain, which can only be generated with a secret key; therefore, anyone with a copy of that key has control of the bitcoin. ((("witnesses")))The digital signature used to spend funds is also referred to as a _witness_, a term used in cryptography. The witness data in a bitcoin transaction testifies to the true ownership of the funds being spent.
((("public and private keys", "key pairs")))((("public and private keys", see="also keys and addresses")))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.
((("public and private keys", "key pairs")))((("public and private keys", see="also keys and addresses")))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 _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.
@ -20,7 +20,7 @@ First, we will introduce cryptography and explain the mathematics used in bitcoi
((("keys and addresses", "overview of", "public key cryptography")))((("digital currencies", "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 cryptography.
In bitcoin, we use public key cryptography to create a key pair that controls access to bitcoin. The key pair consists of a private key and--derived from it--a unique public key. The public key is used to receive funds, and the private key is used to sign transactions to spend the funds.
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.
((("keys and addresses", "overview of", "private key generation")))((("warnings and cautions", "private key protection")))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 bitcoin by proving ownership of funds used in a transaction. The private key must remain secret at all times, because revealing it to third parties is equivalent to giving them control over the bitcoin secured by that key. The private key must also be backed up and protected from accidental loss, because if it's lost it cannot be recovered and the funds secured by it are forever lost, too.
((("keys and addresses", "overview of", "private key generation")))((("warnings and cautions", "private key protection")))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 bitcoin by proving ownership of funds used in a transaction. The private key must remain secret at all times, because revealing it to third parties is equivalent to giving them control over the bitcoin secured by that key. The private key must also be backed up and protected from accidental loss, because if it's lost it cannot be recovered and the funds secured by it are forever lost, too.
[TIP]
====
@ -61,7 +61,7 @@ The bitcoin private key is just a number. You can pick your private keys randoml
The first and most important step in generating keys is to find a secure source of entropy, or randomness. Creating a bitcoin key is essentially the same as "Pick a number between 1 and 2^256^." The exact method you use to pick that number does not matter as long as it is not predictable or repeatable. Bitcoin software uses the underlying operating system's random number generators to produce 256 bits of entropy (randomness). Usually, the OS random number generator is initialized by a human source of randomness, which is why you may be asked to wiggle your mouse around for a few seconds.
More precisely, the private key can be any number between +0+ and +n - 1+ inclusive, where n is a constant (n = 1.158 * 10^77^, slightly less than 2^256^) defined as the order of the elliptic curve used in bitcoin (see <<elliptic_curve>>). To create such a key, we randomly pick a 256-bit number and check that it is less than +n+. In programming terms, this is usually achieved by feeding a larger string of random bits, collected from a cryptographically secure source of randomness, into the SHA256 hash algorithm, which will conveniently produce a 256-bit number. If the result is less than +n+, we have a suitable private key. Otherwise, we simply try again with another random number.
[WARNING]
====
((("random numbers", "random number generation")))((("entropy", "random number generation")))Do not write your own code to create a random number or use a "simple" random number generator offered by your programming language. Use a cryptographically secure pseudorandom number generator (CSPRNG) with a seed from a source of sufficient entropy. Study the documentation of the random number generator library you choose to make sure it is cryptographically secure. Correct implementation of the CSPRNG is critical to the security of the keys.
The +dumpprivkey+ command opens the wallet and extracts the private key that was generated by the +getnewaddress+ command. It is not possible for +bitcoind+ to know the private key from the public key unless they are both stored in the wallet.
The +dumpprivkey+ command opens the wallet and extracts the private key that was generated by the +getnewaddress+ command. It is not possible for +bitcoind+ to know the private key from the public key unless they are both stored in the wallet.
The +dumpprivkey+ command does not generate a private key from a public key, as this is impossible. The command simply reveals the private key that is already known to the wallet and which was generated by the +getnewaddress+ command.
The +dumpprivkey+ command does not generate a private key from a public key, as this is impossible. The command simply reveals the private key that is already known to the wallet and which was generated by the +getnewaddress+ command.
You can also use the Bitcoin Explorer command-line tool (see <<appdx_bx>>) to generate and display private keys with the commands +seed+, +ec-new+, and +ec-to-wif+:
You can also use the Bitcoin Explorer command-line tool (see <<appdx_bx>>) to generate and display private keys with the commands +seed+, +ec-new+, and +ec-to-wif+:
((("keys and addresses", "overview of", "public key calculation")))((("generator point")))The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: _K_ = _k_ * _G_, where _k_ is the private key, _G_ is a constant point called the _generator point_, and _K_ is the resulting public key. The reverse operation, known as "finding the discrete logarithm"—calculating _k_ if you know __K__—is as difficult as trying all possible values of _k_, i.e., a brute-force search. Before we demonstrate how to generate a public key from a private key, let's look at elliptic curve cryptography in a bit more detail.
((("keys and addresses", "overview of", "public key calculation")))((("generator point")))The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: _K_ = _k_ * _G_, where _k_ is the private key, _G_ is a constant point called the _generator point_, and _K_ is the resulting public key. The reverse operation, known as "finding the discrete logarithm"—calculating _k_ if you know __K__—is as difficult as trying all possible values of _k_, i.e., a brute-force search. Before we demonstrate how to generate a public key from a private key, let's look at elliptic curve cryptography in a bit more detail.
[TIP]
====
@ -116,7 +116,7 @@ Elliptic curve multiplication is a type of function that cryptographers call a "
[[elliptic_curve]]
==== Elliptic Curve Cryptography Explained
((("keys and addresses", "overview of", "elliptic curve cryptography")))((("elliptic curve cryptography", id="eliptic04")))((("cryptography", "elliptic curve cryptography", id="Celliptic04")))Elliptic curve cryptography is a type of asymmetric or public key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve.
((("keys and addresses", "overview of", "elliptic curve cryptography")))((("elliptic curve cryptography", id="eliptic04")))((("cryptography", "elliptic curve cryptography", id="Celliptic04")))Elliptic curve cryptography is a type of asymmetric or public key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve.
<<ecc-curve>> is an example of an elliptic curve, similar to that used by bitcoin.
@ -134,7 +134,7 @@ Bitcoin uses a specific elliptic curve and set of mathematical constants, as def
\end{equation}
++++
or
or
[latexmath]
++++
@ -143,9 +143,9 @@ or
\end{equation}
++++
The _mod p_ (modulo prime number p) indicates that this curve is over a finite field of prime order _p_, also written as latexmath:[\( \mathbb{F}_p \)], where p = 2^256^ – 2^32^ – 2^9^ – 2^8^ – 2^7^ – 2^6^ – 2^4^ – 1, a very large prime number.
The _mod p_ (modulo prime number p) indicates that this curve is over a finite field of prime order _p_, also written as latexmath:[\( \mathbb{F}_p \)], where p = 2^256^ – 2^32^ – 2^9^ – 2^8^ – 2^7^ – 2^6^ – 2^4^ – 1, a very large prime number.
Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical to that of an elliptic curve over real numbers. As an example, <<ecc-over-F17-math>> shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid.
Because this curve is defined over a finite field of prime order instead of over the real numbers, it looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical to that of an elliptic curve over real numbers. As an example, <<ecc-over-F17-math>> shows the same elliptic curve over a much smaller finite field of prime order 17, showing a pattern of dots on a grid. The +secp256k1+ bitcoin elliptic curve can be thought of as a much more complex pattern of dots on a unfathomably large grid.
So, for example, the following is a point P with coordinates (x,y) that is a point on the +secp256k1+ curve:
----
P = (55066263022277343669578718895168534326250603453777594175500187360389116729240, 32670510020758816978083085130507043184471273380659243275938904335757337482424)
P = (55066263022277343669578718895168534326250603453777594175500187360389116729240, 32670510020758816978083085130507043184471273380659243275938904335757337482424)
----
<<example_4_1>> shows how you can check this yourself using Python:
@ -190,14 +190,14 @@ In some cases (i.e., if P~1~ and P~2~ have the same x values but different y val
If P~1~ is the "point at infinity," then P~1~ + P~2~ = P~2~. Similarly, if P~2~ is the point at infinity, then P~1~ + P~2~ = P~1~. This shows how the point at infinity plays the role of zero.
It turns out that pass:[+] is associative, which means that (A pass:[+] B) pass:[+] C = A pass:[+] (B pass:[+] C). That means we can write A pass:[+] B pass:[+] C without parentheses and without ambiguity.
It turns out that pass:[+] is associative, which means that (A pass:[+] B) pass:[+] C = A pass:[+] (B pass:[+] C). That means we can write A pass:[+] B pass:[+] C without parentheses and without ambiguity.
Now that we have defined addition, we can define multiplication in the standard way that extends addition. For a point P on the elliptic curve, if k is a whole number, then kP = P + P + P + ... + P (k times). Note that k is sometimes confusingly called an "exponent" in this case.((("", startref="eliptic04")))((("", startref="Celliptic04")))
Now that we have defined addition, we can define multiplication in the standard way that extends addition. For a point P on the elliptic curve, if k is a whole number, then kP = P + P + P + ... + P (k times). Note that k is sometimes confusingly called an "exponent" in this case.((("", startref="eliptic04")))((("", startref="Celliptic04")))
[[public_key_derivation]]
==== Generating a Public Key
==== Generating a Public Key
((("keys and addresses", "overview of", "public key generation")))((("generator point")))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:
((("keys and addresses", "overview of", "public key generation")))((("generator point")))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]
++++
@ -206,7 +206,7 @@ Now that we have defined addition, we can define multiplication in the standard
\end{equation}
++++
where _k_ is the private key, _G_ is the generator point, and _K_ is the resulting public key, a point on the curve. Because the generator point is always the same for all bitcoin users, a private key _k_ multiplied with _G_ will always result in the same public key _K_. The relationship between _k_ and _K_ is fixed, but can only be calculated in one direction, from _k_ to _K_. That's why a bitcoin address (derived from _K_) can be shared with anyone and does not reveal the user's private key (_k_).
where _k_ is the private key, _G_ is the generator point, and _K_ is the resulting public key, a point on the curve. Because the generator point is always the same for all bitcoin users, a private key _k_ multiplied with _G_ will always result in the same public key _K_. The relationship between _k_ and _K_ is fixed, but can only be calculated in one direction, from _k_ to _K_. That's why a bitcoin address (derived from _K_) can be shared with anyone and does not reveal the user's private key (_k_).
[TIP]
====
@ -222,7 +222,7 @@ K = 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD * G
Public key _K_ is defined as a point +K = (x,y)+:
----
K = (x, y)
K = (x, y)
where,
@ -230,7 +230,7 @@ x = F028892BAD7ED57D2FB57BF33081D5CFCF6F9ED3D3D7F159C2E2FFF579DC341A
y = 07CF33DA18BD734C600B96A72BBC4749D5141C90EC8AC328AE52DDFE2E505BDB
----
To visualize multiplication of a point with an integer, we will use the simpler elliptic curve over real numbers—remember, the math is the same. Our goal is to find the multiple _kG_ of the generator point _G_, which is the same as adding _G_ to itself, _k_ times in a row. In elliptic curves, adding a point to itself is the equivalent of drawing a tangent line on the point and finding where it intersects the curve again, then reflecting that point on the x-axis.
To visualize multiplication of a point with an integer, we will use the simpler elliptic curve over real numbers—remember, the math is the same. Our goal is to find the multiple _kG_ of the generator point _G_, which is the same as adding _G_ to itself, _k_ times in a row. In elliptic curves, adding a point to itself is the equivalent of drawing a tangent line on the point and finding where it intersects the curve again, then reflecting that point on the x-axis.
<<ecc_illustrated>> shows the process for deriving _G_, _2G_, _4G_, as a geometric operation on the curve.
The bitcoin address is what appears most commonly in a transaction as the "recipient" of the funds. If we compare a bitcoin transaction to a paper check, the bitcoin address is the beneficiary, which is what we write on the line after "Pay to the order of." On a paper check, that beneficiary can sometimes be the name of a bank account holder, but can also include corporations, institutions, or even cash. Because paper checks do not need to specify an account, but rather use an abstract name as the recipient of funds, they are very flexible 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.
((("addresses", "algorithms used to create")))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, in 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.
((("addresses", "algorithms used to create")))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, in 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:
@ -265,18 +265,18 @@ Starting with the public key _K_, we compute the SHA256 hash and then compute th
\end{equation}
++++
where _K_ is the public key and _A_ is the resulting bitcoin address.
where _K_ is the public key and _A_ is the resulting bitcoin address.
[TIP]
====
A bitcoin address is _not_ the same as a public key. Bitcoin addresses are derived from a public key using a one-way function.
A bitcoin address is _not_ the same as a public key. Bitcoin addresses are derived from a public key using a one-way function.
====
Bitcoin addresses are almost always encoded as "Base58Check" (see <<base58>>), which uses 58 characters (a Base58 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_address>> illustrates the conversion of a public key into a bitcoin address.
[[pubkey_to_address]]
.Public key to bitcoin address: conversion of a public key into a bitcoin address
.Public key to bitcoin address: conversion of a public key into a bitcoin address
image::images/mbc2_0405.png["pubkey_to_address"]
[[base58]]
@ -298,12 +298,12 @@ To add extra security against typos or transcription errors, Base58Check is a Ba
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 in <<base58check_versions>>.
Next, we compute the "double-SHA" checksum, meaning we apply the SHA256 hash-algorithm twice on the previous result (prefix and data):
----
checksum = SHA256(SHA256(prefix+data))
checksum = SHA256(SHA256(prefix+data))
----
From the resulting 32-byte hash (hash-of-a-hash), we take only the first four bytes. These four bytes serve as the error-checking code, or checksum. The checksum is concatenated (appended) to the end.
From the resulting 32-byte hash (hash-of-a-hash), we take only the first four bytes. These four bytes serve as the error-checking code, or checksum. The checksum is concatenated (appended) to the end.
The result is composed of three items: a prefix, the data, and a checksum. This result is encoded using the Base58 alphabet described previously. <<base58check_encoding>> illustrates the Base58Check encoding process.
@ -318,12 +318,12 @@ In bitcoin, most of the data presented to the user is Base58Check-encoded to mak
@ -451,7 +451,7 @@ The resulting WIF-compressed format starts with a "K." This denotes that the pri
===== Public key formats
((("public and private keys", "public key formats")))Public keys are also presented in different ways, usually as either _compressed_ or _uncompressed_ public keys.
((("public and private keys", "public key formats")))Public keys are also presented in different ways, usually as either _compressed_ or _uncompressed_ public keys.
As we saw previously, the public key is a point on the elliptic curve consisting of a pair of coordinates +(x,y)+. It is usually presented with the prefix +04+ followed by two 256-bit numbers: one for the _x_ coordinate of the point, the other for the _y_ coordinate. The prefix +04+ is used to distinguish uncompressed public keys from compressed public keys that begin with a +02+ or a +03+.
@ -479,7 +479,7 @@ K = 04F028892BAD7ED57D2FB57BF33081D5CFCF6F9ED3D3D7F159C2E2FFF579DC341A↵
As we saw in the section <<pubkey>>, a public key is a point (x,y) on an elliptic curve. Because the curve expresses a mathematical function, a point on the curve represents a solution to the equation and, therefore, if we know the _x_ coordinate we can calculate the _y_ coordinate by solving the equation y^2^ mod p = (x^3^ + 7) mod p. That allows us to store only the _x_ coordinate of the public key point, omitting the _y_ coordinate and reducing the size of the key and the space required to store it by 256 bits. An almost 50% reduction in size in every transaction adds up to a lot of data saved over time!
Whereas uncompressed public keys have a prefix of +04+, compressed public keys start with either a +02+ or a +03+ prefix. Let's look at why there are two possible prefixes: because the left side of the equation is __y__^2^, the solution for _y_ is a square root, which can have a positive or negative value. Visually, this means that the resulting _y_ coordinate can be above or below the x-axis. As you can see from the graph of the elliptic curve in <<ecc-curve>>, the curve is symmetric, meaning it is reflected like a mirror by the x-axis. So, while we can omit the _y_ coordinate we have to store the _sign_ of _y_ (positive or negative); or in other words, we have to remember if it was above or below the x-axis because each of those options represents a different point and a different public key. When calculating the elliptic curve in binary arithmetic on the finite field of prime order p, the _y_ coordinate is either even or odd, which corresponds to the positive/negative sign as explained earlier. Therefore, to distinguish between the two possible values of _y_, we store a compressed public key with the prefix +02+ if the _y_ is even, and +03+ if it is odd, allowing the software to correctly deduce the _y_ coordinate from the _x_ coordinate and uncompress the public key to the full coordinates of the point. Public key compression is illustrated in <<pubkey_compression>>.
Whereas uncompressed public keys have a prefix of +04+, compressed public keys start with either a +02+ or a +03+ prefix. Let's look at why there are two possible prefixes: because the left side of the equation is __y__^2^, the solution for _y_ is a square root, which can have a positive or negative value. Visually, this means that the resulting _y_ coordinate can be above or below the x-axis. As you can see from the graph of the elliptic curve in <<ecc-curve>>, the curve is symmetric, meaning it is reflected like a mirror by the x-axis. So, while we can omit the _y_ coordinate we have to store the _sign_ of _y_ (positive or negative); or in other words, we have to remember if it was above or below the x-axis because each of those options represents a different point and a different public key. When calculating the elliptic curve in binary arithmetic on the finite field of prime order p, the _y_ coordinate is either even or odd, which corresponds to the positive/negative sign as explained earlier. Therefore, to distinguish between the two possible values of _y_, we store a compressed public key with the prefix +02+ if the _y_ is even, and +03+ if it is odd, allowing the software to correctly deduce the _y_ coordinate from the _x_ coordinate and uncompress the public key to the full coordinates of the point. Public key compression is illustrated in <<pubkey_compression>>.
[[pubkey_compression]]
[role="smallerseventy"]
@ -496,7 +496,7 @@ This compressed public key corresponds to the same private key, meaning it is ge
Compressed public keys are gradually becoming the default across bitcoin clients, which is having a significant impact on reducing the size of transactions and therefore the blockchain. However, not all clients support compressed public keys yet. Newer clients that support compressed public keys have to account for transactions from older clients that do not support compressed public keys. This is especially important when a wallet application is importing private keys from another bitcoin wallet application, because the new wallet needs to scan the blockchain to find transactions corresponding to these imported keys. Which bitcoin addresses should the bitcoin wallet scan for? The bitcoin addresses produced by uncompressed public keys, or the bitcoin addresses produced by compressed public keys? Both are valid bitcoin addresses, and can be signed for by the private key, but they are different addresses!
To resolve this issue, when private keys are exported from a wallet, the WIF that is used to represent them is implemented differently in newer bitcoin wallets, to indicate that these private keys have been used to produce _compressed_ public keys and therefore _compressed_ bitcoin addresses. This allows the importing wallet to distinguish between private keys originating from older or newer wallets and search the blockchain for transactions with bitcoin addresses corresponding to the uncompressed, or the compressed, public keys, respectively. Let's look at how this works in more detail, in the next section.
To resolve this issue, when private keys are exported from a wallet, the WIF that is used to represent them is implemented differently in newer bitcoin wallets, to indicate that these private keys have been used to produce _compressed_ public keys and therefore _compressed_ bitcoin addresses. This allows the importing wallet to distinguish between private keys originating from older or newer wallets and search the blockchain for transactions with bitcoin addresses corresponding to the uncompressed, or the compressed, public keys, respectively. Let's look at how this works in more detail, in the next section.
[[comp_priv]]
===== Compressed private keys
@ -520,7 +520,7 @@ Notice that the hex-compressed private key format has one extra byte at the end
Remember, these formats are _not_ used interchangeably. In a newer wallet that implements compressed public keys, the private keys will only ever be exported as WIF-compressed (with a _K_ or _L_ prefix). If the wallet is an older implementation and does not use compressed public keys, the private keys will only ever be exported as WIF (with a 5 prefix). The goal here is to signal to the wallet importing these private keys whether it must search the blockchain for compressed or uncompressed public keys and addresses.
If a bitcoin wallet is able to implement compressed public keys, it will use those in all transactions. The private keys in the wallet will be used to derive the public key points on the curve, which will be compressed. The compressed public keys will be used to produce bitcoin addresses and those will be used in transactions. When exporting private keys from a new wallet that implements compressed public keys, the WIF is modified, with the addition of a one-byte suffix +01+ to the private key. The resulting Base58Check-encoded private key is called a "compressed WIF" and starts with the letter _K_ or _L_, instead of starting with "5" as is the case with WIF-encoded (noncompressed) keys from older wallets.
If a bitcoin wallet is able to implement compressed public keys, it will use those in all transactions. The private keys in the wallet will be used to derive the public key points on the curve, which will be compressed. The compressed public keys will be used to produce bitcoin addresses and those will be used in transactions. When exporting private keys from a new wallet that implements compressed public keys, the WIF is modified, with the addition of a one-byte suffix +01+ to the private key. The resulting Base58Check-encoded private key is called a "compressed WIF" and starts with the letter _K_ or _L_, instead of starting with "5" as is the case with WIF-encoded (noncompressed) keys from older wallets.
[TIP]
@ -528,7 +528,7 @@ If a bitcoin wallet is able to implement compressed public keys, it will use tho
"Compressed private keys" is a misnomer! They are not compressed; rather, WIF-compressed signifies that the keys should only be used to derive compressed public keys and their corresponding bitcoin addresses. Ironically, a "WIF-compressed" encoded private key is one byte longer because it has the added +01+ suffix to distinguish it from an "uncompressed" one.((("", startref="KAaddress04")))
====
=== Implementing Keys and Addresses in Python
=== Implementing Keys and Addresses in Python
((("keys and addresses", "implementing in Python", id="KApython04")))((("pybitcointools")))The most comprehensive bitcoin library in Python is https://github.com/vbuterin/pybitcointools[pybitcointools] by Vitalik Buterin. In <<key-to-address_script>>, we use the pybitcointools library (imported as "bitcoin") to generate and display keys and addresses in various formats.
<<ec_math>> ((("random numbers", "os.urandom", see="entropy")))((("entropy", "os.urandom", see="random numbers")))((("random numbers", "random number generation")))((("entropy", "random number generation")))uses +os.urandom+, which reflects a cryptographically secure random number generator (CSRNG) provided by the underlying operating system. In the case of a Unix-like operating system such as Linux, it draws from +/dev/urandom+; and in the case of Windows, it calls +CryptGenRandom()+. If a suitable randomness source is not found, +NotImplementedError+ will be raised. While the random number generator used here is for demonstration purposes, it is _not_ appropriate for generating production-quality bitcoin keys as it is not implemented with sufficient security.((("", startref="KApython04")))
<<ec_math>> ((("random numbers", "os.urandom", see="entropy")))((("entropy", "os.urandom", see="random numbers")))((("random numbers", "random number generation")))((("entropy", "random number generation")))uses +os.urandom+, which reflects a cryptographically secure random number generator (CSRNG) provided by the underlying operating system. Caution: Depending on the OS, +os.urandom+ may _not_ be implemented with sufficient security or seeded properly and may _not_ be appropriate for generating production-quality bitcoin keys.((("", startref="KApython04")))
BTC public key: 029ade3effb0a67d5c8609850d797366af428f4a0d5194cb221d807770a1522873
@ -616,18 +616,18 @@ BTC public key: 029ade3effb0a67d5c8609850d797366af428f4a0d5194cb221d807770a15228
==== Encrypted Private Keys (BIP-38)
((("bitcoin improvement proposals", "Encrypted Private Keys (BIP-38)")))((("keys and addresses", "advanced forms", "encrypted private keys")))((("public and private keys", "encrypted private keys")))((("passwords", "encrypted private keys")))((("security", "passwords")))Private keys must remain secret. The need for _confidentiality_ of the private keys is a truism that is quite difficult to achieve in practice, because it conflicts with the equally important security objective of _availability_. Keeping the private key private is much harder when you need to store backups of the private key to avoid losing it. A private key stored in a wallet that is encrypted by a password might be secure, but that wallet needs to be backed up. At times, users need to move keys from one wallet to another—to upgrade or replace the wallet software, for example. Private key backups might also be stored on paper (see <<paper_wallets>>) or on external storage media, such as a USB flash drive. But what if the backup itself is stolen or lost? These conflicting security goals led to the introduction of a portable and convenient standard for encrypting private keys in a way that can be understood by many different wallets and bitcoin clients, standardized by BIP-38 (see <<appdxbitcoinimpproposals>>).
BIP-38 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 kept 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 NIST and used broadly in data encryption implementations for commercial and military applications.
((("bitcoin improvement proposals", "Encrypted Private Keys (BIP-38)")))((("keys and addresses", "advanced forms", "encrypted private keys")))((("public and private keys", "encrypted private keys")))((("passwords", "encrypted private keys")))((("security", "passwords")))Private keys must remain secret. The need for _confidentiality_ of the private keys is a truism that is quite difficult to achieve in practice, because it conflicts with the equally important security objective of _availability_. Keeping the private key private is much harder when you need to store backups of the private key to avoid losing it. A private key stored in a wallet that is encrypted by a password might be secure, but that wallet needs to be backed up. At times, users need to move keys from one wallet to another—to upgrade or replace the wallet software, for example. Private key backups might also be stored on paper (see <<paper_wallets>>) or on external storage media, such as a USB flash drive. But what if the backup itself is stolen or lost? These conflicting security goals led to the introduction of a portable and convenient standard for encrypting private keys in a way that can be understood by many different wallets and bitcoin clients, standardized by BIP-38 (see <<appdxbitcoinimpproposals>>).
BIP-38 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 kept 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 NIST and used broadly in data encryption implementations for commercial and military applications.
A BIP-38 encryption scheme takes as input a bitcoin private key, usually encoded in the WIF, as a Base58Check string with the prefix of "5." Additionally, the BIP-38 encryption scheme takes a passphrase—a long password—usually composed of several words or a complex string of alphanumeric characters. The result of the BIP-38 encryption scheme is a Base58Check-encoded encrypted private key that begins with the prefix +6P+. If you see a key that starts with +6P+, 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 BIP-38-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 http://bitaddress.org[Bit Address] (Wallet Details tab), can be used to decrypt BIP-38 keys.
A BIP-38 encryption scheme takes as input a bitcoin private key, usually encoded in the WIF, as a Base58Check string with the prefix of "5." Additionally, the BIP-38 encryption scheme takes a passphrase—a long password—usually composed of several words or a complex string of alphanumeric characters. The result of the BIP-38 encryption scheme is a Base58Check-encoded encrypted private key that begins with the prefix +6P+. If you see a key that starts with +6P+, 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 BIP-38-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 http://bitaddress.org[Bit Address] (Wallet Details tab), can be used to decrypt BIP-38 keys.
The most common use case for BIP-38 encrypted keys is for paper wallets that can be used to back up private keys on a piece of paper. As long as the user selects a strong passphrase, a paper wallet with BIP-38 encrypted private keys is incredibly secure and a great way to create offline bitcoin storage (also known as "cold storage").
Test the encrypted keys in <<table_4-10>> using bitaddress.org to see how you can get the decrypted key by entering the passphrase.
@ -636,18 +636,18 @@ Test the encrypted keys in <<table_4-10>> using bitaddress.org to see how you ca
[[p2sh_addresses]]
==== Pay-to-Script Hash (P2SH) and Multisig Addresses
==== Pay-to-Script Hash (P2SH) and Multisig Addresses
((("keys and addresses", "advanced forms", "pay-to-script hash and multisig addresses")))((("Pay-to-Script-Hash (P2SH)", "multisig addresses and")))((("multisig addresses")))((("addresses", "multisig addresses")))As we know, traditional bitcoin addresses begin with the number “1” and are derived from the public key, which is derived from the private key. Although anyone can send bitcoin to a “1” address, that bitcoin can only be spent by presenting the corresponding private key signature and public key hash.
((("keys and addresses", "advanced forms", "pay-to-script hash and multisig addresses")))((("Pay-to-Script-Hash (P2SH)", "multisig addresses and")))((("multisig addresses")))((("addresses", "multisig addresses")))As we know, traditional bitcoin addresses begin with the number “1” and are derived from the public key, which is derived from the private key. Although anyone can send bitcoin to a “1” address, that bitcoin can only be spent by presenting the corresponding private key signature and public key hash.
((("bitcoin improvement proposals", "Pay to Script Hash (BIP-16)")))Bitcoin addresses that begin with the number “3” are pay-to-script hash (P2SH) addresses, sometimes erroneously called multisignature or multisig addresses. They designate the beneficiary of a bitcoin transaction as the hash of a script, instead of the owner of a public key. The feature was introduced in January 2012 with BIP-16 (see <<appdxbitcoinimpproposals>>), and is being widely adopted because it provides the opportunity to add functionality to the address itself. Unlike transactions that "send" funds to traditional “1” bitcoin addresses, also known as a pay-to-public-key-hash (P2PKH), funds sent to “3” addresses require something more than the presentation of one public key hash and one private key signature as proof of ownership. The requirements are designated at the time the address is created, within the script, and all inputs to this address will be encumbered with the same requirements.
A P2SH address is created from a transaction script, which defines who can spend a transaction output (for more details, see <<p2sh>>). Encoding a P2SH address involves using the same double-hash function as used during creation of a bitcoin address, only applied on the script instead of the public key:
----
script hash = RIPEMD160(SHA256(script))
----
The resulting "script hash" is encoded with Base58Check with a version prefix of 5, which results in an encoded address starting with a +3+. An example of a P2SH address is +3F6i6kwkevjR7AsAd4te2YB2zZyASEm1HM+, which can be derived using the Bitcoin Explorer commands +script-encode+, +sha256+, +ripemd160+, and +base58check-encode+ (see <<appdx_bx>>) as follows:
P2SH is not necessarily the same as a multisignature standard transaction. A P2SH address _most often_ represents a multi-signature script, but it might also represent a script encoding other types of transactions.
P2SH is not necessarily the same as a multisignature standard transaction. A P2SH address _most often_ represents a multi-signature script, but it might also represent a script encoding other types of transactions.
====
===== Multisignature addresses and P2SH
Currently, the most common implementation of the P2SH function is the multi-signature address script. As the name implies, the underlying script requires more than one signature to prove ownership and therefore spend funds. The bitcoin multi-signature feature is designed to require M signatures (also known as the “threshold”) from a total of N keys, known as an M-of-N multisig, where M is equal to or less than N. For example, Bob the coffee shop owner from <<ch01_intro_what_is_bitcoin>> could use a multisignature address requiring 1-of-2 signatures from a key belonging to him and a key belonging to his spouse, ensuring either of them could sign to spend a transaction output locked to this address. This would be similar to a “joint account” as implemented in traditional banking where either spouse can spend with a single signature. Or Gopesh,((("use cases", "offshore contract services"))) the web designer paid by Bob to create a website, might have a 2-of-3 multisignature address for his business that ensures that no funds can be spent unless at least two of the business partners sign a transaction.
Currently, the most common implementation of the P2SH function is the multi-signature address script. As the name implies, the underlying script requires more than one signature to prove ownership and therefore spend funds. The bitcoin multi-signature feature is designed to require M signatures (also known as the “threshold”) from a total of N keys, known as an M-of-N multisig, where M is equal to or less than N. For example, Bob the coffee shop owner from <<ch01_intro_what_is_bitcoin>> could use a multisignature address requiring 1-of-2 signatures from a key belonging to him and a key belonging to his spouse, ensuring either of them could sign to spend a transaction output locked to this address. This would be similar to a “joint account” as implemented in traditional banking where either spouse can spend with a single signature. Or Gopesh,((("use cases", "offshore contract services"))) the web designer paid by Bob to create a website, might have a 2-of-3 multisignature address for his business that ensures that no funds can be spent unless at least two of the business partners sign a transaction.
We will explore how to create transactions that spend funds from P2SH (and multi-signature) addresses in <<transactions>>.
==== Vanity Addresses
((("keys and addresses", "advanced forms", "vanity addresses")))((("vanity addresses", id="vanity04")))((("addresses", "vanity addresses", id="Avanity04")))Vanity addresses are valid bitcoin addresses that contain human-readable messages. For example, +1LoveBPzzD72PUXLzCkYAtGFYmK5vYNR33+ is a valid address that contains the letters forming the word "Love" as the first four Base-58 letters. Vanity addresses require generating and testing billions of candidate private keys, until a bitcoin address with the desired pattern is found. Although there are some optimizations in the vanity generation algorithm, the process essentially involves picking a private key at random, deriving the public key, deriving the bitcoin address, and checking to see if it matches the desired vanity pattern, repeating billions of times until a match is found.
((("keys and addresses", "advanced forms", "vanity addresses")))((("vanity addresses", id="vanity04")))((("addresses", "vanity addresses", id="Avanity04")))Vanity addresses are valid bitcoin addresses that contain human-readable messages. For example, +1LoveBPzzD72PUXLzCkYAtGFYmK5vYNR33+ is a valid address that contains the letters forming the word "Love" as the first four Base-58 letters. Vanity addresses require generating and testing billions of candidate private keys, until a bitcoin address with the desired pattern is found. Although there are some optimizations in the vanity generation algorithm, the process essentially involves picking a private key at random, deriving the public key, deriving the bitcoin address, and checking to see if it matches the desired vanity pattern, repeating billions of times until a match is found.
Once a vanity address matching the desired pattern is found, the private key from which it was derived can be used by the owner to spend bitcoin in exactly the same way as any other address. Vanity addresses are no less or more secure than any other address. They depend on the same Elliptic Curve Cryptography (ECC) and SHA as any other address. You can no more easily find the private key of an address starting with a vanity pattern than you can any other address.
In <<ch01_intro_what_is_bitcoin>>, we introduced Eugenia, a children's charity director operating in the Philippines. Let's say that Eugenia is organizing a bitcoin fundraising drive and wants to use a vanity bitcoin address to publicize the fundraising. Eugenia will create a vanity address that starts with "1Kids" to promote the children's charity fundraiser. Let's see how this vanity address will be created and what it means for the security of Eugenia's charity.((("use cases", "charitable donations", startref="eugeniafour")))
In <<ch01_intro_what_is_bitcoin>>, we introduced Eugenia, a children's charity director operating in the Philippines. Let's say that Eugenia is organizing a bitcoin fundraising drive and wants to use a vanity bitcoin address to publicize the fundraising. Eugenia will create a vanity address that starts with "1Kids" to promote the children's charity fundraiser. Let's see how this vanity address will be created and what it means for the security of Eugenia's charity.((("use cases", "charitable donations", startref="eugeniafour")))
===== Generating vanity addresses
@ -699,7 +699,7 @@ Let's look at the pattern "1Kids" as a number and see how frequently we might fi
|=======
| Length | Pattern | Frequency | Average search time
| 1 | 1K | 1 in 58 keys | < 1 milliseconds
| 2 | 1Ki| 1 in 3,364 | 50 milliseconds
| 2 | 1Ki| 1 in 3,364 | 50 milliseconds
| 3 | 1Kid | 1 in 195,000 | < 2 seconds
| 4 | 1Kids | 1 in 11 million | 1 minute
| 5 | 1KidsC | 1 in 656 million | 1 hour
@ -712,9 +712,9 @@ Let's look at the pattern "1Kids" as a number and see how frequently we might fi
|=======
As you can see, Eugenia won't be creating the vanity address "1KidsCharity" anytime soon, even if she 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 GPUs. These are often repurposed bitcoin mining "rigs" that are no longer profitable for bitcoin mining but can be used to find vanity addresses. Vanity searches on GPU systems are many orders of magnitude faster than on a general-purpose CPU.
As you can see, Eugenia won't be creating the vanity address "1KidsCharity" anytime soon, even if she 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 GPUs. These are often repurposed bitcoin mining "rigs" that are no longer profitable for bitcoin mining but can be used 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 http://vanitypool.appspot.com[Vanity Pool]. 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 at the time of this writing), Eugenia can outsource the search for a seven-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 http://vanitypool.appspot.com[Vanity Pool]. 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 at the time of this writing), Eugenia can outsource the search for a seven-character pattern vanity address and get results in a few hours instead of having to run a CPU search for months.
Generating a vanity address is a brute-force exercise: try a random key, check the resulting address to see if it matches the desired pattern, repeat until successful. <<vanity_miner_code>> shows an example of a "vanity miner," a program designed to find vanity addresses, written in C++. The example uses the libbitcoin library, which we introduced in <<alt_libraries>>.
@ -764,9 +764,9 @@ The example code will take a few seconds to find a match for the three-character
===== Vanity address security
((("security", "vanity addresses")))Vanity addresses can be used to enhance _and_ to defeat security measures; they are truly a double-edged sword. Used to improve security, a distinctive address makes it harder for adversaries to substitute their own address and fool your customers into paying them instead of you. Unfortunately, vanity addresses also make it possible for anyone to create an address that _resembles_ any random address, or even another vanity address, thereby fooling your customers.
((("security", "vanity addresses")))Vanity addresses can be used to enhance _and_ to defeat security measures; they are truly a double-edged sword. Used to improve security, a distinctive address makes it harder for adversaries to substitute their own address and fool your customers into paying them instead of you. Unfortunately, vanity addresses also make it possible for anyone to create an address that _resembles_ any random address, or even another vanity address, thereby fooling your customers.
Eugenia could advertise a randomly generated address (e.g., +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy+) to which people can send their donations. Or, she could generate a vanity address that starts with 1Kids, to make it more distinctive.
Eugenia could advertise a randomly generated address (e.g., +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy+) to which people can send their donations. Or, she could generate a vanity address that starts with 1Kids, to make it more distinctive.
In both cases, one of the risks of using a single fixed address (rather than a separate dynamic address per donor) is that a thief might be able to infiltrate your website and replace it with his own address, thereby diverting donations to himself. If you have advertised your donation address in a number of different places, your users may visually inspect the address before making a payment to ensure it is the same one they saw on your website, on your email, and on your flyer. In the case of a random address like +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy+, the average user will perhaps inspect the first few characters "1J7mdg" and be satisfied that the address matches. Using a vanity address generator, someone with the intent to steal by substituting a similar-looking address can quickly generate addresses that match the first few characters, as shown in <<table_4-13>>.
@ -779,12 +779,12 @@ In both cases, one of the risks of using a single fixed address (rather than a s
So does a vanity address increase security? If Eugenia generates the vanity address +1Kids33q44erFfpeXrmDSz7zEqG2FesZEN+, users are likely to look at the vanity pattern word _and a few characters beyond_, for example noticing the "1Kids33" part of the address. That would force an attacker to generate a vanity address matching at least six characters (two more), expending an effort that is 3,364 times (58 × 58) higher than the effort Eugenia expended for her 4-character vanity. Essentially, the effort Eugenia expends (or pays a vanity pool for) "pushes" the attacker into having to produce a longer pattern vanity. If Eugenia pays a pool to generate an 8-character vanity address, the attacker would be pushed into the realm of 10 characters, which is infeasible on a personal computer and expensive even with a custom vanity-mining rig or vanity pool. What is affordable for Eugenia becomes unaffordable for the attacker, especially if the potential reward of fraud is not high enough to cover the cost of the vanity address generation.((("", startref="Avanity04")))((("", startref="vanity04")))((("", startref="eugeniafour")))
So does a vanity address increase security? If Eugenia generates the vanity address +1Kids33q44erFfpeXrmDSz7zEqG2FesZEN+, users are likely to look at the vanity pattern word _and a few characters beyond_, for example noticing the "1Kids33" part of the address. That would force an attacker to generate a vanity address matching at least six characters (two more), expending an effort that is 3,364 times (58 × 58) higher than the effort Eugenia expended for her 4-character vanity. Essentially, the effort Eugenia expends (or pays a vanity pool for) "pushes" the attacker into having to produce a longer pattern vanity. If Eugenia pays a pool to generate an 8-character vanity address, the attacker would be pushed into the realm of 10 characters, which is infeasible on a personal computer and expensive even with a custom vanity-mining rig or vanity pool. What is affordable for Eugenia becomes unaffordable for the attacker, especially if the potential reward of fraud is not high enough to cover the cost of the vanity address generation.((("", startref="Avanity04")))((("", startref="vanity04")))((("", startref="eugeniafour")))
[[paper_wallets]]
==== Paper Wallets
((("keys and addresses", "advanced forms", "paper wallets")))((("paper wallets", id="paperw04")))((("wallets", "types of", "paper wallets", id="Wpaper04")))Paper wallets are bitcoin private keys printed on paper. Often the paper wallet also includes the corresponding bitcoin address for convenience, but this is not necessary because it can be derived from the private key. Paper wallets are a very effective way to create backups or offline bitcoin storage, also known as "cold storage." As a backup mechanism, a paper wallet can provide security against the loss of key due to a computer mishap such as a hard-drive failure, theft, or accidental deletion. As a "cold storage" mechanism, if the paper wallet keys are generated offline and never stored on a computer system, they are much more secure against hackers, keyloggers, and other online computer threats.
((("keys and addresses", "advanced forms", "paper wallets")))((("paper wallets", id="paperw04")))((("wallets", "types of", "paper wallets", id="Wpaper04")))Paper wallets are bitcoin private keys printed on paper. Often the paper wallet also includes the corresponding bitcoin address for convenience, but this is not necessary because it can be derived from the private key. Paper wallets are a very effective way to create backups or offline bitcoin storage, also known as "cold storage." As a backup mechanism, a paper wallet can provide security against the loss of key due to a computer mishap such as a hard-drive failure, theft, or accidental deletion. As a "cold storage" mechanism, if the paper wallet keys are generated offline and never stored on a computer system, they are much more secure against hackers, keyloggers, and other online computer threats.
Paper wallets come in many shapes, sizes, and designs, but at a very basic level are just a key and an address printed on paper. <<table_4-14>> shows the simplest form of a paper wallet.
@ -803,7 +803,7 @@ Paper wallets can be generated easily using a tool such as the client-side JavaS
.An example of a simple paper wallet from bitaddress.org
image::images/mbc2_0408.png[]
((("bitcoin improvement proposals", "Encrypted Private Keys (BIP-38)")))The disadvantage of a 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 bitcoin locked with those keys. A more sophisticated paper wallet storage system uses BIP-38 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. <<paper_wallet_encrypted>> shows a paper wallet with an encrypted private key (BIP-38) created on the bitaddress.org site.
((("bitcoin improvement proposals", "Encrypted Private Keys (BIP-38)")))The disadvantage of a 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 bitcoin locked with those keys. A more sophisticated paper wallet storage system uses BIP-38 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. <<paper_wallet_encrypted>> shows a paper wallet with an encrypted private key (BIP-38) created on the bitaddress.org site.
[[paper_wallet_encrypted]]
.An example of an encrypted paper wallet from bitaddress.org. The passphrase is "test."
@ -824,7 +824,7 @@ image::images/mbc2_0410.png[]
.The bitcoinpaperwallet.com paper wallet with the private key concealed
image::images/mbc2_0411.png[]
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.((("", startref="KAadvanced04")))((("", startref="Wpaper04")))((("", startref="paperw04")))
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.((("", startref="KAadvanced04")))((("", startref="Wpaper04")))((("", startref="paperw04")))
[[paper_wallet_spw]]
.An example of a paper wallet with additional copies of the keys on a backup "stub"
Andreas M. Antonopoulos
6 years ago