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[[ch04_wallets_keys]]
== Wallets, Keys and Addresses
Ownership of bitcoin is established through _digital keys_ and _digital signatures_. These keys are not actually stored in the network, but are instead created and stored by end-users, in a file called a _wallet_, or in a database. The 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. The keys themselves are completely independent of the bitcoin protocol and can be generated and managed by the end users. Keys can be generated without reference to the blockchain or access to the network. Keys enable many of the interesting properties of bitcoin, including de-centralized trust and control, ownership attestation and the cryptographic-proof security model. Keys can also be converted into unique and public addresses (eg. bitcoin addresses, those that start with a "1"), allowing anyone to create transactions that transfer ownership of bitcoin to our keys.
Ownership of bitcoin is established through _digital keys_ and _digital signatures_. These keys are not actually stored in the network, but are instead created and stored by end-users in a file called a _wallet_ or in a database. The 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. The keys themselves are completely independent of the bitcoin protocol and can be generated and managed by the end users. Keys can be generated without reference to the blockchain or access to the network. Keys enable many of the interesting properties of bitcoin, including de-centralized trust and control, ownership attestation and the cryptographic-proof security model. Keys can also be converted into unique and public addresses (i.e. bitcoin addresses that start with a "1"), allowing anyone to create transactions that transfer ownership of bitcoin to our keys.
In this chapter we will introduce wallets, which contain cryptographic keys. We will look at how keys are generated, stored and managed. We will review the various encoding formats used to represent private and public keys, addresses and script addresses. Finally we will look at special uses of keys to sign messages, prove ownerhsip and special addresses uses such as 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 ownerhsip and to create vanity addresses and paper wallets.
[TIP]
====
Wallets contain keys, not coins. The coins are stored on the blockchain, in the form of transaction-outputs (often noted as vout or txout). Each user has a wallet containing keys. Wallets are really keychains containing pairs of private/publice keys (See <<public key>>). Users sign transactions with the keys, thereby proving they own the transaction outputs (their coins).
Wallets contain keys, not coins. The coins are stored on the blockchain in the form of transaction outputs (often noted as vout or txout). Each user has a wallet containing keys. Wallets are really keychains containing pairs of private/publice keys (See <<public key>>). Users sign transactions with the keys, thereby proving they own the transaction outputs (their coins).
====
[[wallets]]
@ -24,16 +24,16 @@ In the most simple form, the +private key+ is a number. The private key be used
===== Generating a private key from a random number
A private key is a number, between +1+ and +n - 1+ where latexmath:[\(n = 1.158 * 10^\(77\) \)] is the order of the elliptic curve used in bitcoin (See <<secp256k1>>). To create such a key, we just pick a 256-bit random number, and check that it is less than +n - 1+. The constant +n+ is defined in any elliptic curve cryptography library. 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 SHA-256 hash algorithm which will conveniently produce a 256-bit number.
A private key is a number between +1+ and +n - 1+ where latexmath:[\(n = 1.158 * 10^\(77\) \)] is the order of the elliptic curve used in bitcoin (See <<secp256k1>>). To create such a key, we just pick a 256-bit random number and check that it is less than +n - 1+. The constant +n+ is defined in any elliptic curve cryptography library. 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 SHA-256 hash algorithm which will conveniently produce a 256-bit number.
[TIP]
====
Do not try and design your own pseudo random number generator (PRNG). Use a cryptographically-secure (CSPRNG) with a seed from a source of sufficient entropy, the choice of which which depends on you operating-system. Correct implementation of the CSPRNG is critical to the security of the keys. DIY is highly discouraged unless you are a professional cryptographer.
Do not try and design your own pseudo random number generator (PRNG). Use a cryptographically-secure (CSPRNG) with a seed from a source of sufficient entropy, the choice of which which depends on the operating system. Correct implementation of the CSPRNG is critical to the security of the keys. DIY is highly discouraged unless you are a professional cryptographer.
====
Below, is a randomly generated private key shown in hexadecimal format (256 binary digits, or bits is shown as 64 hexadecimal digits, each 4-bits):
Below, is a randomly generated private key shown in hexadecimal format (256 binary digits is shown as 64 hexadecimal digits, each 4 bits):
----
1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD
@ -102,7 +102,7 @@ KxFC1jmwwCoACiCAWZ3eXa96mBM6tb3TYzGmf6YwgdGWZgawvrtJ
==== From Private Key to Public Key
The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: latexmath:[\(K = k * G\)]+ where +k+ is the private key, +G+ is a constant point called the _Generator Point_ and +K+ is the resulting public key. The reverse (division), or calculating +k+ if you know +K+ is as difficult as trying all possible values of +k+, ie a brute-force search.
The public key is calculated from the private key using elliptic curve multiplication, which is irreversible: latexmath:[\(K = k * G\)]+ where +k+ is the private key, +G+ is a constant point called the _Generator Point_ and +K+ is the resulting public key. The reverse (division), or calculating +k+ if you know +K+ is as difficult as trying all possible values of +k+, i.e. a brute-force search.
The public key is a point on the elliptic curve, and consists of a pair of coordinates +(x,y)+, normally represented by a 512-bit number with the added prefix +04+.
@ -137,7 +137,7 @@ A private key can be converted into a public key, but a public key cannot be con
==== From Public Key to Address
An address is a string of digits and characters that can be shared with anyone who wants to send you money. In bitcoin, addresses begin with the digit "1". An address made by hashing the public key twice, through two different hashing algorithms.
An address is a string of digits and characters that can be shared with anyone who wants to send you money. In bitcoin, addresses begin with the digit "1". This is an address made by hashing the public key twice through two different hashing algorithms.
==== Generating keys
@ -145,12 +145,12 @@ There are many ways to generate keys for use in bitcoin. The simplest is to pick
[TIP]
====
The private key is just a number. A public key can be generated from any private key. Therefore, a public key can be generated from any number, up to 256-bits long. You can pick your keys randomly using a method as simple as tossing 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. Keys really are just a pair of numbers, one calculated from the other.
The private key is just a number. A public key can be generated from any private key. Therefore, a public key can be generated from any number, up to 256 bits long. You can pick your keys randomly using a method as simple as tossing 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. Keys really are just a pair of numbers, one calculated from the other.
====
===== Type-0 or non-deterministic (random) keys
The first and most important step in generating keys is to find a secure source of entropy, or randomness. The private key is a 256-bit number, which must be selected at random. 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 will use the underlying operating system's random number generators to produce 256-bits of entropy. 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. For the trully paranoid, nothing beats dice, pencil and paper.
The first and most important step in generating keys is to find a secure source of entropy, or randomness. The private key is a 256-bit number, which must be selected at random. 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 will use the underlying operating system's random number generators to produce 256 bits of entropy. 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. For the truly paranoid, nothing beats dice, pencil and paper.
[[Type0_keygen]]
@ -160,7 +160,7 @@ image::images/Type-0 keygen.png["Private key generation"]
[TIP]
====
The bitcoin private key is just a number. A public key can be generated from any private key. Therefore, a public key can be generated from any number, up to 256-bits long. You can pick your keys randomly using a method as simple as dice, pencil and paper.
The bitcoin private key is just a number. A public key can be generated from any private key. Therefore, a public key can be generated from any number, up to 256 bits long. You can pick your keys randomly using a method as simple as dice, pencil and paper.
====
Once a private key has been generated, the public key equivalent can be derived from it using the elliptic curve multiplication function. Many software implementations of bitcoin use the OpenSSL library, specifically the https://www.openssl.org/docs/crypto/ec.html[Elliptic Curve library].
@ -170,7 +170,7 @@ Once a private key has been generated, the public key equivalent can be derived
The size of bitcoin's private key, 2^256^ is a truly unfathomable number. It is equal to approximately 10^77^ in decimal. The visible universe contains approximately 10^80^ atoms.
====
This most basic form of key generation, generates what are known as _Type-0_ or _Non-Deterministic_ (ie. random) keys. When a sequence of keys is generated for a single user's wallet, each key is randomly generated when needed
This most basic form of key generation generates what are known as _Type-0_ or _Non-Deterministic_ (i.e. random) keys. When a sequence of keys is generated for a single user's wallet, each key is randomly generated when needed.
[[Type0_chain]]
.Type-0 or Non-Deterministic Keys are randomly generated as needed
@ -205,7 +205,7 @@ image::images/BIP32-derivation.png["Key generation"]
[[public_key]]
==== Public key cryptography and crypto-currency
((("public key")))
Public-key cryptography, is like a digital padlock, which can only be opened by the owner of a secret, also known as a private key. The owner of that key can hand out as many copies of the padlock, as they want, and others can use it to "lock" bitcoins inside transactions recorded on the blockchain. Only the owner of the private key can then create a signature to unlock and "redeem" these transactions, as only they can open the digital padlock.
Public-key cryptography is like a digital padlock which can only be opened by the owner of a secret, also known as a private key. The owner of that key can hand out as many copies of the padlock as they want, and others can use it to "lock" bitcoins inside transactions recorded on the blockchain. Only the owner of the private key can then create a signature to unlock and "redeem" these transactions, as only they can open the digital padlock.
When Alice pays Bob 15 millibits (0.015 BTC), she is unlocking a set of unspent outputs with _digital signatures_ made with her _private keys_. Like signing a check, she signs a transaction to authorize spending her coins. Then she "locks" a certain amount of bitcoin with Bob's address (made from his _public key_ and freely shared), thereby making a transaction output encumbered by Bob's address and spendable only with Bob's signature.
@ -213,7 +213,7 @@ Spending can be visualized as unlocking my coins and then locking some of them w
==== Public Key Cryptography
((("public key", "private key")))
Public key, or assymetric cryptography, is a type of cryptography that uses a pair of digital keys. A user has a private and a public key. The public key is derived from the private key with a mathematical function that is difficult to reverse.
Public key (or asymmetric) cryptography is a type of cryptography that uses a pair of digital keys. A user has a private and a public key. The public key is derived from the private key with a mathematical function that is difficult to reverse.
[[pubcrypto_colors]]
.Public Key Cryptography: Irreversible Function as Color Mixing
@ -225,12 +225,12 @@ To use public key cryptography, Alice will ask Bob for his public key. Then, Ali
[TIP]
====
In most implementations, the private and public keys are stored together as a _key pair_, for convenience. However, it is trivial to re-produce the public key if one has the private key, so storing only the private key is also possible.
In most implementations, the private and public keys are stored together as a _key pair_ for convenience. However, it is trivial to reproduce the public key if one has the private key, so storing only the private key is also possible.
====
==== Elliptic Curve Cryptography
((("elliptic curve cryptography", "ECC")))
Elliptic Curve Cryptography is a type of assymetric or public-key cryptography based on the discrete logarithm problem as expressed by addition and multiplication on the points of an elliptic curve.
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.
Starting with a private key in the form of a randomly generator number +k+, we multiply it with 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+.
@ -278,7 +278,7 @@ image::images/ecc-over-F37-math.png["Addition operator on points of an elliptic
Once a private key has been generated, the public key equivalent can be derived from it using the elliptic curve multiplication function. Many software implementations of bitcoin use the OpenSSL library, specifically the https://www.openssl.org/docs/crypto/ec.html[Elliptic Curve library].
Here's an example from the reference implementation, generating a public key from an existing private key
Here's an example of the reference implementation generating a public key from an existing private key.
[[ecc_mult]]
.Reference Client: Using OpenSSL's EC_POINT_mul to generate the public key from a private key https://github.com/bitcoin/bitcoin/blob/0.8.4/src/key.cpp#L31[bitcoin/src/key.cpp : 31]