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drusselloctal@gmail.com 2014-10-30 11:51:23 -07:00
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@ -659,35 +659,35 @@ The parent public key, chain code, and the index number are combined and hashed
.Extending a parent private key to create a child private key
image::images/msbt_0411.png["ChildPrivateDerivation"]
Changing the index allows us to extend the parent and create the other children in the sequence, e.g. Child 0, Child 1, Child 2 etc. Each parent key can have 2 billion children keys.
Changing the index allows us to extend the parent and create the other children in the sequence, e.g., Child 0, Child 1, Child 2, etc. Each parent key can have 2 billion children keys.
Repeating the process one level down the tree, each child can in turn become a parent and create its own children, in an infinite number of generations.
===== Using derived child keys
Child private keys are indistinguishable from non-deterministic (random) keys. Because the derivation function is a one way function, the child key cannot be used to find the parent key. The child key can also not be used to find any siblings. If you have the n~th~ child, you cannot find its siblings, such as the n-1 child or the n+1 child, or any other children that are part of the sequence. Only the parent key and chain code can derive all the children. Without the child chain code, the child key cannot be used to derive any grandchildren either. You need both the child private key and the child chain code to start a new branch and derive grandchildren.
Child private keys are indistinguishable from non-deterministic (random) keys. Because the derivation function is a one-way function, the child key cannot be used to find the parent key. The child key can also not be used to find any siblings. If you have the n~th~ child, you cannot find its siblings, such as the n–1 child or the n+1 child, or any other children that are part of the sequence. Only the parent key and chain code can derive all the children. Without the child chain code, the child key cannot be used to derive any grandchildren either. You need both the child private key and the child chain code to start a new branch and derive grandchildren.
So what can the child private key be used for on its own? It can be used to make a public key and a bitcoin address. Then, it can be used to sign transactions to spend anything paid to that address.
[TIP]
====
A child private key, the corresponding public key and the bitcoin address are all indistinguishable from keys and addresses created randomly. The fact that they are part of a sequence is not visible, outside of the HD wallet function that created them. Once created, they operate exactly as "normal" keys.
A child private key, the corresponding public key, and the bitcoin address are all indistinguishable from keys and addresses created randomly. The fact that they are part of a sequence is not visible, outside of the HD wallet function that created them. Once created, they operate exactly as "normal" keys.
====
===== Extended keys
As we saw above, the key derivation function can be used to create children at any level of the tree, based on the three inputs: a key, a chain code and the index of the desired child. The two essential ingredients are the key and chain code and combined these are called an _extended key_. The term "extended key" could also be thought of as "extensible key" because such a key can be used to derive children.
As we saw earlier, the key derivation function can be used to create children at any level of the tree, based on the three inputs: a key, a chain code and the index of the desired child. The two essential ingredients are the key and chain code, and combined these are called an _extended key_. The term "extended key" could also be thought of as "extensible key" because such a key can be used to derive children.
Extended keys are stored and represented simply as the concatenation of the 256 bit key and 256 bit chain code into a 512 bit sequence. There are two types of extended keys: An extended private key is the combination of a private key and chain code and can be used to derive child private keys (and from them, child public keys). An extended public key is a public key and chain code, which can be used to create child public keys, as described in <<public_key_derivation>>.
Extended keys are stored and represented simply as the concatenation of the 256-bit key and 256-bit chain code into a 512-bit sequence. There are two types of extended keys. An extended private key is the combination of a private key and chain code and can be used to derive child private keys (and from them, child public keys). An extended public key is a public key and chain code, which can be used to create child public keys, as described in <<public_key_derivation>>.
Think of an extended key as the root of a branch in the tree structure of the HD wallet. With the root of the branch, you can derive the rest of the branch. The extended private key can create a complete branch, whereas the extended public key can only create a branch of public keys.
[TIP]
====
An extended key consists of a private or public key and chain code. An extended key can create children generating its own branch in the tree structure. Sharing an extended key gives access to the entire branch.
An extended key consists of a private or public key and chain code. An extended key can create children, generating its own branch in the tree structure. Sharing an extended key gives access to the entire branch.
====
Extended keys are encoded using Base58Check, to easily export and import between different BIP0032 compatible wallets. The Base58Check coding for extended keys uses a special version number that results in the prefix "xprv" and "xpub" when encoded in base 58 characters, to make them easily recognizable. Since the extended key is 512 or 513 bits, it is also much longer than other Base58Check encoded strings we have seen previously.
Extended keys are encoded using Base58Check, to easily export and import between different BIP0032 compatible wallets. The Base58Check coding for extended keys uses a special version number that results in the prefix "xprv" and "xpub" when encoded in Base58 characters, to make them easily recognizable. Because the extended key is 512 or 513 bits, it is also much longer than other Base58Check-encoded strings we have seen previously.
Here's an example of an extended private key, encoded in Base58Check:
----
@ -703,15 +703,15 @@ xpub67xpozcx8pe95XVuZLHXZeG6XWXHpGq6Qv5cmNfi7cS5mtjJ2tgypeQbBs2UAR6KECeeMVKZBPLr
[[public__child_key_derivation]]
===== Public child key derivation
As mentioned above, a very useful characteristic of hierarchical deterministic wallets is the ability to derive public child keys from public parent keys, _without_ having the private keys. This gives us two ways to derive a child public key: either from the child private key, or directly from the parent public key.
As mentioned previously, a very useful characteristic of hierarchical deterministic wallets is the ability to derive public child keys from public parent keys, _without_ having the private keys. This gives us two ways to derive a child public key: either from the child private key, or directly from the parent public key.
An extended public key can be used, therefore, to derive all of the _public_ keys (and only the public keys) in that branch of the HD wallet structure.
This shortcut can be used to create very secure public-key-only deployments where a server or application has a copy of an extended public key and no private keys whatsoever. That kind of deployment can produce an infinite number of public keys and bitcoin addresses but cannot spend any of the money sent to those addresses. Meanwhile, on another more secure server, the extended private key can derive all the corresponding private keys to sign transactions and spend the money.
This shortcut can be used to create very secure public-key-only deployments where a server or application has a copy of an extended public key and no private keys whatsoever. That kind of deployment can produce an infinite number of public keys and bitcoin addresses, but cannot spend any of the money sent to those addresses. Meanwhile, on another more secure server, the extended private key can derive all the corresponding private keys to sign transactions and spend the money.
One common application of this solution is to install an extended public key on a web server that serves an e-commerce application. The web server can use the public key derivation function to create a new bitcoin address for every transaction (e.g. for a customer shopping cart). The web server will not have any private keys that would be vulnerable to theft. Without HD wallets, the only way to do this is to generate thousands of bitcoin addresses on a separate secure server and then pre-load them on the e-commerce server. That approach is cumbersome and requires constant maintenance to ensure that the e-commerce server doesn't "run out" of keys.
One common application of this solution is to install an extended public key on a web server that serves an e-commerce application. The web server can use the public key derivation function to create a new bitcoin address for every transaction (e.g., for a customer shopping cart). The web server will not have any private keys that would be vulnerable to theft. Without HD wallets, the only way to do this is to generate thousands of bitcoin addresses on a separate secure server and then preload them on the ecommerce server. That approach is cumbersome and requires constant maintenance to ensure that the ecommerce server doesn't "run out" of keys.
Another common application of this solution is for cold-storage or hardware wallets. In that scenario, the extended private key can be stored on a paper wallet or hardware device (such as a Trezor hardware wallet), while the extended public key can be kept online. The user can create "receive" addresses at will, while the private keys are safely stored offline. To spend the funds, they can use the extended private key on an offline signing bitcoin client or sign transactions on the hardware wallet device (e.g. Trezor).
Another common application of this solution is for cold-storage or hardware wallets. In that scenario, the extended private key can be stored on a paper wallet or hardware device (such as a Trezor hardware wallet), while the extended public key can be kept online. The user can create "receive" addresses at will, while the private keys are safely stored offline. To spend the funds, the user can use the extended private key on an offline signing bitcoin client or sign transactions on the hardware wallet device (e.g., Trezor). <<CKDpub>> illustrates the mechanism for extending a parent public key to derive child public keys.
[[CKDpub]]
.Extending a parent public key to create a child public key
@ -721,27 +721,27 @@ image::images/msbt_0412.png["ChildPublicDerivation"]
The ability to derive a branch of public keys from an extended public key is very useful, but it comes with a potential risk. Access to an extended public key does not give access to child private keys. However, because the extended public key contains the chain code, if a child private key is known, or somehow leaked, it can be used with the chain code to derive all the other child private keys. A single leaked child private key, together with a parent chain code, reveals all the private keys of all the children. Worse, the child private key together with a parent chain code can be used to deduce the parent private key.
To counter this risk, HD wallets use an alternative derivation function called _hardened derivation_, which "breaks" the relationship between parent public key and child chain code. The hardened derivation function uses the parent private key to derive the child chain code, instead of the parent public key. This creates a "firewall" in the parent/child sequence, with a chain code that cannot be used to compromise a parent or sibling private key. The hardened derivation function looks almost identical to the normal child private key derivation, except that the parent private key is used as input to the hash function, instead of the parent public key, as shown in the diagram below:
To counter this risk, HD wallets use an alternative derivation function called _hardened derivation_, which "breaks" the relationship between parent public key and child chain code. The hardened derivation function uses the parent private key to derive the child chain code, instead of the parent public key. This creates a "firewall" in the parent/child sequence, with a chain code that cannot be used to compromise a parent or sibling private key. The hardened derivation function looks almost identical to the normal child private key derivation, except that the parent private key is used as input to the hash function, instead of the parent public key, as shown in the diagram in <<CKDprime>>.
[[CKDprime]]
.Hardened derivation of a child key, omits the parent public key
.Hardened derivation of a child key; omits the parent public key
image::images/msbt_0413.png["ChildHardPrivateDerivation"]
When the hardened private derivation function is used, the resulting child private key and chain code are completely different from what would result from the normal derivation function. The resulting "branch" of keys can be used to produce extended public keys which are not vulnerable, since the chain code they contain cannot be exploited to reveal any private keys. Hardened derivation is therefore used to create a "gap" in the tree above the level where extended public keys are used.
When the hardened private derivation function is used, the resulting child private key and chain code are completely different from what would result from the normal derivation function. The resulting "branch" of keys can be used to produce extended public keys that are not vulnerable, because the chain code they contain cannot be exploited to reveal any private keys. Hardened derivation is therefore used to create a "gap" in the tree above the level where extended public keys are used.
In simple terms, if you want to use the convenience of an extended public key to derive branches of public keys, without exposing yourself to the risk of a leaked chain code, you should derive it from a hardened parent, rather than a normal parent. As a best practice, the level-1 children of the master keys are always derived through the hardened derivation, to prevent compromise of the master keys.
===== Index numbers for normal and hardened derivation
The index number used in the derivation function is a 32-bit integer. To easily distinguish between keys derived through the normal derivation function versus keys derived through hardened derivation, this index number is split into two ranges. Index numbers between 0 and 2^31^-1 (0x0 to 0x7FFFFFFF) are used _only_ for normal derivation. Index numbers between 2^31^ and 2^32^-1 (0x80000000 to 0xFFFFFFFF) are used _only_ for hardened derivation. Therefore, if the index number is less than 2^31^, that means the child is normal, whereas if the index number is equal or above 2^31^, the child is hardened.
The index number used in the derivation function is a 32-bit integer. To easily distinguish between keys derived through the normal derivation function versus keys derived through hardened derivation, this index number is split into two ranges. Index numbers between 0 and 2^31^–1 (0x0 to 0x7FFFFFFF) are used _only_ for normal derivation. Index numbers between 2^31^ and 2^32^–1 (0x80000000 to 0xFFFFFFFF) are used _only_ for hardened derivation. Therefore, if the index number is less than 2^31^, that means the child is normal, whereas if the index number is equal or above 2^31^, the child is hardened.
To make the index number easier to read and display, the index number for hardened children is displayed starting from zero, but with a prime symbol. The first normal child key is therefore displayed as 0, whereas the first hardened child (index 0x80000000) is displayed as 0'. In sequence then, the second hardened key would have index 0x80000001 and would be displayed as 1', and so on. When you see an HD wallet index i', that means 2^31^+i.
===== HD wallet key identifier (path)
Keys in an HD wallet are identified using a "path" naming convention, with each level of the tree separated by a slash (/) character. Private keys derived from the master private key start with "m". Public keys derived from the master public key start with "M". Therefore, the first child private key of the master private key is m/0. The first child public key is M/0. The second grandchild of the first child is m/0/1 and so on.
Keys in an HD wallet are identified using a "path" naming convention, with each level of the tree separated by a slash (/) character (see Table 4-8). Private keys derived from the master private key start with "m". Public keys derived from the master public key start with "M". Therefore, the first child private key of the master private key is m/0. The first child public key is M/0. The second grandchild of the first child is m/0/1, and so on.
The "ancestry" of a key is read from right to left, until you reach the master key from which it was derived. For example, identifier m/x/y/z describes the key which is the z-th child of key m/x/y, which is the y-th child of key m/x, which is the x-th child of m.
The "ancestry" of a key is read from right to left, until you reach the master key from which it was derived. For example, identifier m/x/y/z describes the key that is the z-th child of key m/x/y, which is the y-th child of key m/x, which is the x-th child of m.
.HD wallet path examples
|=======
@ -754,19 +754,19 @@ The "ancestry" of a key is read from right to left, until you reach the master k
===== Navigating the HD wallet tree structure
The HD wallet tree structure offers tremendous flexibility. Each parent extended key can have 4 billion children: 2 billion normal children and 2 billion hardened children. Each of those children can have another 4 billion children and so on. The tree can be as deep as you want, with an infinite number of generations. With all that flexibility, however, it becomes quite difficult to navigate this infinite tree. It is especially difficult to transfer HD wallets between implementations, because the possibilities for internal organization into branches and sub-branches are endless.
The HD wallet tree structure offers tremendous flexibility. Each parent extended key can have 4 billion children: 2 billion normal children and 2 billion hardened children. Each of those children can have another 4 billion children, and so on. The tree can be as deep as you want, with an infinite number of generations. With all that flexibility, however, it becomes quite difficult to navigate this infinite tree. It is especially difficult to transfer HD wallets between implementations, because the possibilities for internal organization into branches and subbranches are endless.
Two Bitcoin Improvement Proposals (BIPs) offer a solution to this complexity, by creating some proposed standards for the structure of HD wallet trees. BIP0043 proposes the use of the first hardened child index as a special identifier that signifies the "purpose" of the tree structure. Based on BIP0043, an HD wallet should use only one level-1 branch of the tree, with the index number identifying the structure and namespace of the rest of the tree by defining its purpose. For example, an HD wallet using only branch m/i'/, is intended to signify a specific purpose and that purpose is identified by index number "i".
Two Bitcoin Improvement Proposals (BIPs) offer a solution to this complexity, by creating some proposed standards for the structure of HD wallet trees. BIP0043 proposes the use of the first hardened child index as a special identifier that signifies the "purpose" of the tree structure. Based on BIP0043, an HD wallet should use only one level-1 branch of the tree, with the index number identifying the structure and namespace of the rest of the tree by defining its purpose. For example, an HD wallet using only branch m/i'/ is intended to signify a specific purpose and that purpose is identified by index number "i".
Extending that specification, BIP0044 proposes a multi-account structure as "purpose" number +44'+ under BIP0043. All HD wallets following the BIP0044 structure are identified by the fact that they only used one branch of the tree: m/44'/.
Extending that specification, BIP0044 proposes a multiaccount structure as "purpose" number +44'+ under BIP0043. All HD wallets following the BIP0044 structure are identified by the fact that they only used one branch of the tree: m/44'/.
BIP0044 specifies the structure as consisting of five pre-defined tree levels:
+m / purpose' / coin_type' / account' / change / address_index+
The first level "purpose" is always set to +44'+. The second level "coin_type" specifies the type of crypto-currency coin, allowing for multi-currency HD wallets where each currency has its own subtree under the second level. There are three currencies defined for now: Bitcoin is m/44'/0', Bitcoin Testnet is m/44'/1' and Litecoin is m/44'/2'.
The first level "purpose" is always set to +44'+. The second level "coin_type" specifies the type of crypto-currency coin, allowing for multicurrency HD wallets where each currency has its own subtree under the second level. There are three currencies defined for now: Bitcoin is m/44'/0', Bitcoin Testnet is m/44'/1' and Litecoin is m/44'/2'.
The third level of the tree is "account", which allows users to subdivide their wallets into separate logical sub-accounts, for accounting or organizational purposes. For example, an HD wallet might contain two bitcoin "accounts": m/44'/0'/0' and m/44'/0'/1'. Each account is the root of its own sub-tree.
The third level of the tree is "account," which allows users to subdivide their wallets into separate logical subaccounts, for accounting or organizational purposes. For example, an HD wallet might contain two bitcoin "accounts": m/44'/0'/0' and m/44'/0'/1'. Each account is the root of its own subtree.
On the fourth level "change", an HD wallet has two sub-trees, one for creating receiving addresses and one for creating change addresses. Note that whereas the previous levels used hardened derivation, this level uses normal derivation. This is to allow this level of the tree to export extended public keys for use in an non-secured environment. Usable addresses are derived by the HD wallet as children of the fourth level, making the fifth level of the tree the "address_index". For example, the third receiving address for bitcoin payments in the primary account would be M/44'/0'/0'/0/2. Here are a few more examples: