HD wallets¶
Introduction¶
Hierarchical Deterministic(HD) wallets were developed to make it easy to derive many keys from a single “seed.” The most advanced form of deterministic wallets is the HD wallet defined by the BIP-32 standard. HD wallets contain keys derived in a tree structure, such that a parent key can derive a sequence of children keys, each of which can derive a sequence of grandchildren keys, and so on, to an infinite depth.
HD wallets offer two major advantages over random (nondeterministic) keys. First, the tree structure can be used to express additional organizational meaning, such as when a specific branch of subkeys is used to receive incoming payments and a different branch is used to receive change from outgoing payments. Branches of keys can also be used in corporate settings, allocating different branches to departments, subsidiaries, specific functions, or accounting categories.
The second advantage of HD wallets is that users can create a sequence of public keys without having access to the corresponding private keys. This allows HD wallets to be used on an insecure server or in a receive-only capacity, issuing a different public key for each transaction. The public keys do not need to be preloaded or derived in advance, yet the server doesn’t have the private keys that can spend the funds.
Child Key Derivation¶
HD wallets use a child key derivation (CKD) function to derive child keys from parent keys.
The child key derivation functions are based on a one-way hash function that combines:
- A parent private or public key (ECDSA uncompressed key)
- A seed called a chain code (256 bits)
- An index number (32 bits)
The chain code is used to introduce deterministic random data to the process, so that knowing the index and a child key is not sufficient to derive other child keys. Knowing a child key does not make it possible to find its siblings, unless you also have the chain code. The initial chain code seed (at the root of the tree) is made from the seed, while subsequent child chain codes are derived from each parent chain code. These three items (parent key, chain code, and index) are combined and hashed to generate children keys, as follows. The parent public key, chain code, and the index number are combined and hashed with the HMAC-SHA512 algorithm to produce a 512-bit hash. This 512-bit hash is split into two 256-bit halves. The right-half 256 bits of the hash output become the chain code for the child. The left-half 256 bits of the hash are added to the parent private key to produce the child private key. In Extending a parent private key to create a child private key, we see this illustrated with the index set to 0 to produce the “zero” (first by index) child of the parent.
Hardened child key derivation¶
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 Hardened derivation of a child key; omits the parent public key.
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.
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 231–1 (0x0 to 0x7FFFFFFF) are used only for normal derivation. Index numbers between 231 and 232–1 (0x80000000 to 0xFFFFFFFF) are used only for hardened derivation. Therefore, if the index number is less than 231, the child is normal, whereas if the index number is equal or above 231, 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 ” ‘ “ symbol. The first normal child key is therefore displayed as 0, whereas the first hardened child (index 0x80000000) is displayed as 0’.
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 (see HD wallet path examples). 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 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.
BIP-44 specifies the structure as consisting of five predefined tree levels:
- m / purpose’ / coin_type’ / account’ / change / address_index