From 49ee5b2b4361a51b98fee99b0506da46f8cde9f5 Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Mon, 19 May 2014 00:03:22 -0400 Subject: [PATCH 1/6] ch4 reflow --- ch04.asciidoc | 218 +++++++++++++++++++++++--------------------------- 1 file changed, 98 insertions(+), 120 deletions(-) diff --git a/ch04.asciidoc b/ch04.asciidoc index 5396c910..a5b1f3ca 100644 --- a/ch04.asciidoc +++ b/ch04.asciidoc @@ -1,18 +1,83 @@ -[[ch04_wallets_keys]] -== Wallets, Keys and Addresses +[[ch04_keys_addresses_wallets]] +== Keys, Addresses, Wallets -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. +=== 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 network. 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. + +In transactions, the public key is represented by its digital fingeprint called a _bitcoin address_ which is used as the beneficiary name on a cheque (ie. "Pay to the order of"). In most cases a bitcoin address is a generated from and corresponds to a public key. However, like a beneficiary name on a cheque, some bitcoin addresses do not represent a public key and instead represent other beneficiaries such as scripts, as we will see later in this chapter. This way, bitcoin addresses abstract the recipient of funds, making transaction destinations flexible, similar to paper cheques: a single payment instrument that can be used to pay into people's accounts, company accounts, pay for bills or pay to cash. The bitcoin address is the only part of the wallet that users will routinely see. In this chapter we will introduce wallets, which contain cryptographic keys. We will look at how keys are generated, stored and managed. We will review the various encoding formats used to represent private and public keys, addresses and script addresses. Finally we will look at special uses of keys: to sign messages, to prove ownership and to create vanity addresses and paper wallets. + +=== Keys + +==== Public key cryptography and crypto-currency +((("public key"))) +Public key cryptography was invented in the 1970s and is mathematics applied to computer 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. + +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 special relationship between the public key and private key that allows the private key to be used to generate a signature. 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 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 that transaction as valid, meaning the person transfering the bitcoin owned them at the time of the transfer. + [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/public keys (See <>). Users sign transactions with the keys, thereby proving they own the transaction outputs (their coins). +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. ==== -[[wallets]] +==== Elliptic Curve Cryptography +((("elliptic curve cryptography", "ECC"))) +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. -=== Wallets +Starting with a private key in the form of a randomly generated 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+. + +[latexmath] +++++ +\begin{equation} +{K = k * G} +\end{equation} +++++ + +[[key_derivation]] +where +k+ is the private key, +G+ is a fixed point on the curve called the _generator point_, ((("generator point"))) and +K+ is the resulting public key, another point on the curve. + + +[[ecc_addition]] +.Elliptic Curve Cryptography: Visualizing the addition operator on the points of an elliptic curve +image::images/ecc-addition.png["Addition operator on points of an elliptic curve"] + +Bitcoin specifically uses the +secp256k1+ elliptic curve: +((("secp256k1"))) +[latexmath] +++++ +\begin{equation} +{y^2 = (x^3 + 7)} \text{over} \mathbb{F}_p +\end{equation} +++++ +or + +[latexmath] +++++ +\begin{equation} +{y^2 \mod p = (x^3 + 7) \mod p} +\end{equation} +++++ + +where +latexmath:[\(p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1\)]+, a very large prime number. + +The +mod p+ indicates that this curve is over a finite field of prime order +p+, also written as latexmath:[\(\mathbb{F}_p\)]. The curve looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical as that of an elliptic curve over the real numbers shown above. + +[[ecc-over-F37-math]] +.Elliptic Curve Cryptography: Visualizing the addition operator on the points of an elliptic curve over F(p) +image::images/ecc-over-F37-math.png["Addition operator on points of an elliptic curve over F(p)"] + +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]. + + +[TIP] +==== +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. +==== === Keys @@ -139,10 +204,22 @@ 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 begin with the digit "1". This is an address made by hashing the public key twice through two different hashing algorithms. -==== Generating keys +==== Private Keys +==== Public Keys +==== Addresses +==== Key Formats and Addresses +===== Base58 and Base58Check Encoding +===== Compressed Keys +==== Wallets There are many ways to generate keys for use in bitcoin. The simplest is to pick a large random number and turn it into a key pair (See <>). A random key can be generated with very simple hardware or even manually with pen, paper and dice. The disadvantage of random keys is that if you generate many of them you must keep copies of all of them. Another method for making keys is _deterministic key generation_. Here you generate each new key as a function of the previous key, linking them in a sequence. As long as you can re-create that sequence, you only need the first key to generate them all. In this section we will examine the different methods for key generation. +[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/public keys (See <>). Users sign transactions with the keys, thereby proving they own the transaction outputs (their coins). +==== + + [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. @@ -196,116 +273,17 @@ 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. - -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. - -Spending can be visualized as unlocking my coins and then locking some of them with someone else's padlock so they now own them. - -==== Public Key Cryptography -((("public key", "private key"))) -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 -image::images/pubcrypto-colors.png["Public Key Cryptography: Irreversible Function as Color Mixing"] - -As an example, think of mixing a shade of yellow with a shade of blue. Mixing the two colors is simple. However, figuring out exactly which two shades went into the final mix is not so easy, unless you have one of the two shades. If you have one of the colors you can easily filter it out and get the other. Whereas mixing colors is easy, "un-mixing" them is hard. The mathematical equivalent most often used in cryptography is the Discrete Logarithm Problem link$$https://en.wikipedia.org/wiki/Discrete_logarithm_problem#Cryptography$$[Discrete Logarithm Problem in Cryptography] - -To use public key cryptography, Alice will ask Bob for his public key. Then, Alice can encrypt messages with Bob's public key, knowing that only Bob can read those messages, since only Bob has the equivalent private key. - -[TIP] -==== -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 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+. - -[latexmath] -++++ -\begin{equation} -{K = k * G} -\end{equation} -++++ - -[[key_derivation]] -where +k+ is the private key, +G+ is a fixed point on the curve called the _generator point_, ((("generator point"))) and +K+ is the resulting public key, another point on the curve. - -Elliptic curve multiplication can be visualized geometrically as drawing a line connecting two points on the curve (G and kG) to produce a third point (K). The third point is the public key. - -[[ecc_addition]] -.Elliptic Curve Cryptography: Visualizing the addition operator on the points of an elliptic curve -image::images/ecc-addition.png["Addition operator on points of an elliptic curve"] - -Bitcoin specifically uses the +secp256k1+ elliptic curve: -((("secp256k1"))) -[latexmath] -++++ -\begin{equation} -{y^2 = (x^3 + 7)} \text{over} \mathbb{F}_p -\end{equation} -++++ -or - -[latexmath] -++++ -\begin{equation} -{y^2 \mod p = (x^3 + 7) \mod p} -\end{equation} -++++ - -where +latexmath:[\(p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1\)]+, a very large prime number. - -The +mod p+ indicates that this curve is over a finite field of prime order +p+, also written as latexmath:[\(\mathbb{F}_p\)]. The curve looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical as that of an elliptic curve over the real numbers shown above. - -[[ecc-over-F37-math]] -.Elliptic Curve Cryptography: Visualizing the addition operator on the points of an elliptic curve over F(p) -image::images/ecc-over-F37-math.png["Addition operator on points of an elliptic curve over F(p)"] - - -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 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] -==== -[source, c++] ----- - -// Generate a private key from just the secret parameter -int EC_KEY_regenerate_key(EC_KEY *eckey, BIGNUM *priv_key) -{ - -[...initialization code omitted ...] - - if (!EC_POINT_mul(group, pub_key, priv_key, NULL, NULL, ctx)) <1> - goto err; - - EC_KEY_set_private_key(eckey,priv_key); - EC_KEY_set_public_key(eckey,pub_key); - -[...] ----- -<1> Multiplying the priv_key by the generator point of the elliptic curve group, produces the pub_key -==== - -[TIP] -==== -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. -==== - - +===== Non-Deterministic (Random) +===== Deterministic (Seeded) +===== Seed Words (BIP0039) +===== Deterministic Chains (Electrum Key Chains) +===== Deterministic Trees (BIP0032) +==== Key Storage +===== Software Wallets +===== Hardware Wallets +===== Paper Wallets +==== Advanced Keys and Addresses +===== Encrypted Keys (BIP0038) +===== Pay To Script Hash Addresses (P2SH) +===== Multi-Signature Addresses +===== Vanity Addresses \ No newline at end of file From 7d05e1cbbec5d6e03d6a251bf0999a01b5a6e1a4 Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Mon, 19 May 2014 08:33:01 -0400 Subject: [PATCH 2/6] chapter 4 re-flowed, new diagrams, re-written introduction --- ch04.asciidoc | 192 +++++++++++++--------------- images/HD wallet.png | Bin 0 -> 29100 bytes images/chained wallet.png | Bin 0 -> 17682 bytes images/non-deterministic wallet.png | Bin 0 -> 13709 bytes 4 files changed, 91 insertions(+), 101 deletions(-) create mode 100644 images/HD wallet.png create mode 100644 images/chained wallet.png create mode 100644 images/non-deterministic wallet.png diff --git a/ch04.asciidoc b/ch04.asciidoc index a5b1f3ca..9b0aa0ee 100644 --- a/ch04.asciidoc +++ b/ch04.asciidoc @@ -29,17 +29,6 @@ In most implementations, the private and public keys are stored together as a _k ((("elliptic curve cryptography", "ECC"))) 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 generated 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+. - -[latexmath] -++++ -\begin{equation} -{K = k * G} -\end{equation} -++++ - -[[key_derivation]] -where +k+ is the private key, +G+ is a fixed point on the curve called the _generator point_, ((("generator point"))) and +K+ is the resulting public key, another point on the curve. [[ecc_addition]] @@ -104,6 +93,78 @@ Below is a randomly generated private key shown in hexadecimal format (256 binar 1E99423A4ED27608A15A2616A2B0E9E52CED330AC530EDCC32C8FFC6A526AEDD ---- +To generate a new key with bitcoind, use the +getnewaddress+ command. For security reasons it displays the public key only, not the private key. To ask bitcoind to expose the private key, use the +dumpprivkey+ command. Here's an example of both commands: + +---- +$ bitcoind getnewaddress +1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy +$ bitcoind dumpprivkey 1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy +KxFC1jmwwCoACiCAWZ3eXa96mBM6tb3TYzGmf6YwgdGWZgawvrtJ +---- + +The +dumpprivkey+ command is opening the wallet and extracting the private key that was generated by the +getnewaddress+ command. It is not otherwise possible for bitcoind to know the private key from the public key, unless they are both stored in the wallet. In the example above, we see that the private key has a "K" prefix, indicating it is encoded as a WIF-compressed format. This means that the key-pair is stored in the wallet with both keys compressed, saving 31 bytes of space. If the prefix had been "5", indicating the WIF format, we would know that the key-pair is uncompressed. + +You can also use +sx tools+ to generate keys and convert them between formats: + +===== New key +---- +$ sx newkey +5J3mBbAH58CpQ3Y5RNJpUKPE62SQ5tfcvU2JpbnkeyhfsYB1Jcn +---- + +==== Public Keys + +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. + +Starting with a private key in the form of a randomly generated 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+. + +[latexmath] +++++ +\begin{equation} +{K = k * G} +\end{equation} +++++ + +[[key_derivation]] +where +k+ is the private key, +G+ is a fixed point on the curve called the _generator point_, ((("generator point"))) and +K+ is the resulting public key, another point on the curve. + +[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 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+. + +Here's the public key generated by the private key we created above, shown as the coordinates +(x,y)+ + +.Public Key K defined as a point +K = (x,y)+ +---- +x = 32 5D 52 E3 B7 ... E5 D3 78 +y = 7A 3D 41 E6 70 ... CD 90 C2 +---- + +Here's the same public key shown as a 512-bit number (130 hex digits) with the prefix +04+ followed by +x+ and then +y+ + +.Uncompressed Public Key K shown in hex (130 hex digits) as +04 x y+ +---- +K = 04 32 5D 52 E3 B7 ... CD 90 C2 +---- + +[TIP] +==== +A private key can be converted into a public key, but a public key cannot be converted back into a private key because the math only works one way. +==== + +==== Addresses + +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. + +===== Base58 and Base58Check Encoding + +==== Key Formats and Addresses + +===== Private Key Formats + The private key can be represented in a number of different formats, all of which correspond to the same 256-bit number. These formats include: .Private Key Representations (Encoding Formats) @@ -128,24 +189,6 @@ The key above, for example can be represented as: All of the above representations are different ways of showing the same number, the same private key. They look different, but any one format can easily be converted to any other format. -To generate a new key with bitcoind, use the +getnewaddress+ command. For security reasons it displays the public key only, not the private key. To ask bitcoind to expose the private key, use the +dumpprivkey+ command. Here's an example of both commands: - ----- -$ bitcoind getnewaddress -1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy -$ bitcoind dumpprivkey 1J7mdg5rbQyUHENYdx39WVWK7fsLpEoXZy -KxFC1jmwwCoACiCAWZ3eXa96mBM6tb3TYzGmf6YwgdGWZgawvrtJ ----- - -The +dumpprivkey+ command is opening the wallet and extracting the private key that was generated by the +getnewaddress+ command. It is not otherwise possible for bitcoind to know the private key from the public key, unless they are both stored in the wallet. In the example above, we see that the private key has a "K" prefix, indicating it is encoded as a WIF-compressed format. This means that the key-pair is stored in the wallet with both keys compressed, saving 31 bytes of space. If the prefix had been "5", indicating the WIF format, we would know that the key-pair is uncompressed. - -You can also use +sx tools+ to generate keys and convert them between formats: - -===== New key ----- -$ sx newkey -5J3mBbAH58CpQ3Y5RNJpUKPE62SQ5tfcvU2JpbnkeyhfsYB1Jcn ----- ===== Decoded from the Base58Check encoding to Hex ---- @@ -165,26 +208,7 @@ $ sx base58check-encode 1e99423a4ed27608a15a2616a2b0e9e52ced330ac530edcc32c8ffc6 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+, 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+. - -Here's the public key generated by the private key we created above, shown as the coordinates +(x,y)+ - -.Public Key K defined as a point +K = (x,y)+ ----- -x = 32 5D 52 E3 B7 ... E5 D3 78 -y = 7A 3D 41 E6 70 ... CD 90 C2 ----- - -Here's the same public key shown as a 512-bit number (130 hex digits) with the prefix +04+ followed by +x+ and then +y+ - -.Uncompressed Public Key K shown in hex (130 hex digits) as +04 x y+ ----- -K = 04 32 5D 52 E3 B7 ... CD 90 C2 ----- +===== Compressed Keys The +y+ coordinate can be deduced from the +x+ coordinate, since they both lie on the same curved line defined by the elliptic curve equation. This makes it possible to store the public key _compressed_, with the +y+ omitted. A +compressed public key+ has the prefix +02+ if the +y+ is above the x-axis, and +03+ if it is below the x-axis, allowing the software to calculate it from +x+. @@ -195,21 +219,6 @@ Here's the same public key above, shown as a +compressed public key+ stored in 2 K = 02 32 5D 52 E3 B7 ... E5 D3 78 ---- -[TIP] -==== -A private key can be converted into a public key, but a public key cannot be converted back into a private key because the math only works one way. -==== - -==== 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". This is an address made by hashing the public key twice through two different hashing algorithms. - -==== Private Keys -==== Public Keys -==== Addresses -==== Key Formats and Addresses -===== Base58 and Base58Check Encoding -===== Compressed Keys ==== Wallets There are many ways to generate keys for use in bitcoin. The simplest is to pick a large random number and turn it into a key pair (See <>). A random key can be generated with very simple hardware or even manually with pen, paper and dice. The disadvantage of random keys is that if you generate many of them you must keep copies of all of them. Another method for making keys is _deterministic key generation_. Here you generate each new key as a function of the previous key, linking them in a sequence. As long as you can re-create that sequence, you only need the first key to generate them all. In this section we will examine the different methods for key generation. @@ -219,20 +228,14 @@ There are many ways to generate keys for use in bitcoin. The simplest is to pick 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/public keys (See <>). Users sign transactions with the keys, thereby proving they own the transaction outputs (their coins). ==== - -[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. -==== - -===== Type-0 or non-deterministic (random) keys +===== Non-Deterministic (Random) Wallets 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]] -.Private key generation: From random mouse movements to a 256-bit number used as the private key -image::images/Type-0 keygen.png["Private key generation"] +[[Type0_wallet]] +.Type-0 Non-Deterministic (Random) Wallet: A Collection of Randomly Generated Keys +image::images/non-deterministic wallet.png["non-deterministic wallet"] [TIP] @@ -240,8 +243,6 @@ image::images/Type-0 keygen.png["Private key generation"] 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]. - [TIP] ==== 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. @@ -249,35 +250,24 @@ The size of bitcoin's private key, 2^256^ is a truly unfathomable number. It is 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 -image::images/type0_chain.png["Key generation"] - -===== Type-1 deterministic (non-random) key chains - -[[Type1_chain]] -.Type-1 Deterministic Keys are generated from a phrase and index number -image::images/type1_chain.png["Key generation"] - -===== Type-2 chained deterministic keys - -[[Type2_chain]] -.Type-2 Chained Deterministic Keys are generated from a binary seed and index number -image::images/type2_chain.png["Key generation"] - -===== Type-2 hierarchical deterministic keys - -[[Type2_tree]] -.Type-2 Hierarchical Deterministic Keys are derived from a master seed using a tree structure -image::images/BIP32-derivation.png["Key generation"] - - - -===== Non-Deterministic (Random) ===== Deterministic (Seeded) + ===== Seed Words (BIP0039) + ===== Deterministic Chains (Electrum Key Chains) + + +[[Type1_wallet]] +.Type-1 Deterministic Wallet: A Chain of Keys Generared from a Seed +image::images/chained wallet.png["chained wallet"] + + ===== Deterministic Trees (BIP0032) + +[[Type2_wallet]] +.Type-2 Hierarchical Deterministic Wallet: A Tree of Keys Generared from a Seed +image::images/HD wallet.png["HD wallet"] + ==== Key Storage ===== Software Wallets ===== Hardware Wallets diff --git a/images/HD wallet.png b/images/HD wallet.png new file mode 100644 index 0000000000000000000000000000000000000000..18f8adca188e28e17bb05640c8ff48a6040ff798 GIT binary patch literal 29100 zcmdqI_gj-)vj&PHq9P(F@Y2LWld4iek*Y|q(gQ?5YJf*r^q$SDFIS(OPX7LahOumFp!2m< z0^h9}@AMxkq4<%1&!JDQ3z+}ky1 z%r*?YJ^BCBPZmdq*O-KkT4cZ}Dyob{@81(iqd{wfUIwgZvq`nW zep9Y#4nzq%dV2a}>BC;2&kNVPu!+XPg($Ure;b72XNMmWAnm^Q8+R5xoVK?a)2@2` z?%WH}O1s~YDB@*a=@8L3F|k_Vzv+;)GK!LG@LK~8_{Hm?8n=`kg|Xq`1vF^%z^8DB zG+gO;+)8To%V$f?gCdBJ!v3k24t7Mm%abuw_fAPkNvo-masS`2G9KsnQ<&o!lg$r{~#cZf&_A z$DfXN4aMcw=IbXK!3X|ezxJmJ$#S6EpdsqQeZ^R&mDIks}Q 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zg4cs7%QtKkRitW|A?vn^)&96Z>tgirv9)-L} zU+W?ZTE&K@G?~&X^j`_vg*qFcwkEVh`>Xt_95_JNx@k;`phNk>4Yl;TKgkvsvI@tH zPV|>5U_7mSKL54nDd>J56J&)Bub43EXLL1OAz7Vrk#UK2Oj+LB!Hq60Y0!4*i)e8u zhyzX9vjhgXB;s!-$kPfUQa+Y(+-pQcHpdQ&+?(M1!&o9*iJtBVioS|E)PRp}RU3T{ zQGZQxa|(>Uk)!Zo2_fS_@1F9{2+b$)es1^H!5X!*U-rMxu`p-x!x)nS1raz2aAL$Pafr z8yk&Qm4#b-pqh-o08p~?!N>jf53jCUuh=kJ!`yBB+|8cY^6_t)shCV~p5vO4#^wKV zj1NB$w^@qkgsjIuXUN)}<1#gJ?Xq~f^H~7XOFA{6`9yER*S%kAe64aGIXG8W?Q_3d z=aG$uKaHpZ4g8TX9P`Y_cy+pq$}9z?Ya@}!MgSK^b}~C}(P?S`sDexNGN562Y0RHX z)=)8(l(8nxknb{Iyf7!0xJ3URR8*L9BP{jZyP;6Haj_Y+0-XL9BdvwWGJFHyn-k=K zV=H$<>MS7sILxx|RPk-va$V_~_`hVk?9F@OWJy_tU<9@R=2)rmA@@>k2;Le*r;a+A9D6 literal 0 HcmV?d00001 From 2089218eff260142c70cf2120f7eb4fb47ad529c Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Mon, 19 May 2014 08:37:11 -0400 Subject: [PATCH 3/6] renamed images, to remove spaces --- images/{HD wallet.png => HD_wallet.png} | Bin images/{chained wallet.png => chained_wallet.png} | Bin ...stic wallet.png => non-deterministic_wallet.png} | Bin 3 files changed, 0 insertions(+), 0 deletions(-) rename images/{HD wallet.png => HD_wallet.png} (100%) rename images/{chained wallet.png => chained_wallet.png} (100%) rename images/{non-deterministic wallet.png => non-deterministic_wallet.png} (100%) diff --git a/images/HD wallet.png b/images/HD_wallet.png similarity index 100% rename from images/HD wallet.png rename to images/HD_wallet.png diff --git a/images/chained wallet.png b/images/chained_wallet.png similarity index 100% rename from images/chained wallet.png rename to images/chained_wallet.png diff --git a/images/non-deterministic wallet.png b/images/non-deterministic_wallet.png similarity index 100% rename from images/non-deterministic wallet.png rename to images/non-deterministic_wallet.png From 2c8774fe9f19baf168989acb61f9b4f12d6b2250 Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Mon, 19 May 2014 08:37:52 -0400 Subject: [PATCH 4/6] updated image file names in chapter --- ch04.asciidoc | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/ch04.asciidoc b/ch04.asciidoc index 9b0aa0ee..74c06cf1 100644 --- a/ch04.asciidoc +++ b/ch04.asciidoc @@ -235,7 +235,7 @@ The first and most important step in generating keys is to find a secure source [[Type0_wallet]] .Type-0 Non-Deterministic (Random) Wallet: A Collection of Randomly Generated Keys -image::images/non-deterministic wallet.png["non-deterministic wallet"] +image::images/non-deterministic_wallet.png["non-deterministic wallet"] [TIP] @@ -259,14 +259,14 @@ This most basic form of key generation generates what are known as _Type-0_ or _ [[Type1_wallet]] .Type-1 Deterministic Wallet: A Chain of Keys Generared from a Seed -image::images/chained wallet.png["chained wallet"] +image::images/chained_wallet.png["chained wallet"] ===== Deterministic Trees (BIP0032) [[Type2_wallet]] .Type-2 Hierarchical Deterministic Wallet: A Tree of Keys Generared from a Seed -image::images/HD wallet.png["HD wallet"] +image::images/HD_wallet.png["HD wallet"] ==== Key Storage ===== Software Wallets From 7fea35e380a329424ff1b911d4b6cc3d77d3bf9f Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Mon, 19 May 2014 08:40:33 -0400 Subject: [PATCH 5/6] added base58check encoding image and caption --- ch04.asciidoc | 6 ++++++ images/Base58CheckEncoding.png | Bin 0 -> 45537 bytes 2 files changed, 6 insertions(+) create mode 100644 images/Base58CheckEncoding.png diff --git a/ch04.asciidoc b/ch04.asciidoc index 74c06cf1..074d13e7 100644 --- a/ch04.asciidoc +++ b/ch04.asciidoc @@ -161,6 +161,12 @@ An address is a string of digits and characters that can be shared with anyone w ===== Base58 and Base58Check Encoding + +[[base58check_encoding]] +.Base58Check Encoding: A base-58, versioned and checksummed format for unambiguously encoding bitcoin data +image::images/Base58CheckEncoding.png["Base58CheckEncoding"] + + ==== Key Formats and Addresses ===== Private Key Formats diff --git a/images/Base58CheckEncoding.png b/images/Base58CheckEncoding.png new file mode 100644 index 0000000000000000000000000000000000000000..07f8ebc29bfc57392905db40672a5fa57b5a8e3b GIT binary 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zuU$$mYs0RfAlx|^zYb{QiD671QT&f>;?Ku=FOJm@6=r=S7MG>`QP_|YQr!J`yin>F iCezZ!|MMeoUo?4gWj(P$x-C^Z&mZsy_tkoy{P}O&M~?;o literal 0 HcmV?d00001 From a6c47ee88c14b81dd8ccf9fcc57e6e7b3449d48a Mon Sep 17 00:00:00 2001 From: "Andreas M. Antonopoulos" Date: Mon, 19 May 2014 08:44:04 -0400 Subject: [PATCH 6/6] added note to replace ECC diagrams with ones showing correct points --- ch04.asciidoc | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/ch04.asciidoc b/ch04.asciidoc index 074d13e7..5185e371 100644 --- a/ch04.asciidoc +++ b/ch04.asciidoc @@ -29,7 +29,7 @@ In most implementations, the private and public keys are stored together as a _k ((("elliptic curve cryptography", "ECC"))) 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. - +<< Replace chart below with one showing the K = k * G key generation as a line on the curve >> [[ecc_addition]] .Elliptic Curve Cryptography: Visualizing the addition operator on the points of an elliptic curve @@ -56,6 +56,8 @@ where +latexmath:[\(p = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1\)]+, a ve The +mod p+ indicates that this curve is over a finite field of prime order +p+, also written as latexmath:[\(\mathbb{F}_p\)]. The curve looks like a pattern of dots scattered in two dimensions, which makes it difficult to visualize. However, the math is identical as that of an elliptic curve over the real numbers shown above. +<< Replace chart below with one showing the K = k * G key generation as a line on the curve >> + [[ecc-over-F37-math]] .Elliptic Curve Cryptography: Visualizing the addition operator on the points of an elliptic curve over F(p) image::images/ecc-over-F37-math.png["Addition operator on points of an elliptic curve over F(p)"]