This BIP defines a scheme for key derivation that allows for dynamic creation of key hierarchies based on the algorithm described in BIP32.
==Motivation==
Several proposals have been made to try to standardize a structure for hierarchical deterministic wallets for the sake of interoperability (reference BIP32, BIP44, BIP45). However, all proposals to date have tried to impose a specific structure upfront without providing any flexibility for dynamic creation of new hierarchical levels with different semantics or mapping between different applications that use distinct structures.
Instead of attempting to impose a specific structure upfront, this BIP proposes that we design the derivation in such a way that we can continue extending hierarchies arbitrarily and indefinitely.
==Specification==
BIP32 provides a hierarchical derivation scheme where every node in the tree can be either used to derive child nodes or used as a signing key for ECDSA. This means that as soon as we choose to use a node as a signing key, we can no longer derive children from that node. To draw an analogy to file systems, each node is either a file or a directory but never both. However, given the need to predictably know the location of new children, it is generally not a good idea to mix both signing keys and parent nodes at the same level in the hierarchy. This means that as soon as we've decided that a particular level in the hierarchy is to be used for signing keys, we've lost the ability to nest deeper levels into the tree.
At every level of the hierarchy, we reserve the child with index 0 to allow further nesting, and for signing key parent nodes use child indices 1 to MAX_INDEX (2<sup>31</sup> - 1) for signing keys. We can use either hardened or nonhardened derivation.
Let p denote a specific signing key parent node and k be an index greater than 0. The children signing keys are then:
p / k
with k > 0.
To create sublevels, we derive the nested nodes:
p / 0 / n
with n ≥ 0.
Each of these nodes can now contain signing key children of their own, and again we reserve index 0 to allow deeper nesting.
==Notation==
We propose the following shorthand for writing nested node derivations:
p // n instead of p / 0 / n
p //' n instead of p / 0' / n
==Mappings==
Rather than specifying upfront which path is to be used for a specific purpose (i.e. external invoicing vs. internal change), different applications can specify arbitrary parent nodes and derivation paths. This allows for nesting of sublevels to arbitrary depth with application-specified semantics. Rather than trying to specify use cases upfront, we leave the design completely open-ended. Different applications can exchange these mappings for interoperability. Eventually, if certain mappings become popular, application user interfaces can provide convenient shortcuts or use them as defaults.
Note that BIP32 suggests reserving child 0 for the derivation of signing keys rather than sublevels. It is not really necessary to reserve signing key parents, however, as each key's parent's path can be explicitly stated. But unless we reserve a child for sublevel derivation, we lose the ability to nest deeper levels into the hierarchy. While we could reserve any arbitrary index for nesting sublevels, reserving child 0 seems simplest to implement, leaving all indices > 0 for contiguously indexed signing keys. We could also use MAX_INDEX (2<sup>31</sup> - 1) for this purpose. However, we believe doing so introduces more ideosyncracies into the semantics and will present a problem if we ever decide to extend the scheme to use indices larger than 31 bits.
==Use Cases==
===Account Hierarchies===
For all that follows, we assume that key indices k > 0 and parent node indices n ≥ 0.
From a master seed m, we can construct a default account using the following derivations for nonhardened signing keys:
m / 1 / k (for change/internal outputs)
m / 2 / k (for invoice/external outputs)
To create subaccount a<sub>n</sub>, we use:
a<sub>n</sub> = m // n
To generate keys for subaccount a<sub>n</sub>, we use:
a<sub>n</sub> / 1 / k (for change/internal outputs)
a<sub>n</sub> / 2 / k (for invoice/external outputs)
We can continue creating subaccounts indefinitely using this scheme.
===Bidirectional Payment Channels===
In order to create a bidirectional payment channel, it is necessary that previous commitments be revokable. In order to revoke previous commitments, each party reveals a secret to the other that would allow them to steal the funds in the channel if a transaction for a previous commitment is inserted into the blockchain.
By allowing for arbitrary nesting of sublevels, we can construct decision trees of arbitrary depth and revoke an entire branch by revealing a parent node used to derive all the children.
