<pre>
  BIP: 86
  Layer: Applications
  Title: Key Derivation for Single Key P2TR Outputs
  Author: Ava Chow <me@achow101.com>
  Comments-Summary: No comments yet.
  Comments-URI: https://github.com/bitcoin/bips/wiki/Comments:BIP-0086
  Status: Final
  Type: Standards Track
  Created: 2021-06-22
  License: BSD-2-Clause
</pre>

==Abstract==

This document suggests a derivation scheme for HD wallets whose keys are involved in single key
P2TR ([[bip-0341.mediawiki|BIP 341]]) outputs as the Taproot internal key.

===Copyright===

This BIP is licensed under the 2-clause BSD license.

==Motivation==

With the usage of single key P2TR transactions, it is useful to have a common derivation scheme so
that HD wallets that only have a backup of the HD seed can be likely to recover single key Taproot
outputs. Although there are now solutions which obviate the need for fixed derivation paths for
specific script types, many software wallets and hardware signers still use seed backups which
lack derivation path and script information. Thus we largely use the same approach used in BIPs
[[bip-0049.mediawiki|49]] and [[bip-0084.mediawiki|84]] for ease of implementation.

==Specifications==

This BIP defines the two needed steps to derive multiple deterministic addresses based on a
[[bip-0032.mediawiki|BIP 32]] master private key.

===Public key derivation===

To derive a public key from the root account, this BIP uses the same account-structure as
defined in BIPs [[bip-0044.mediawiki|44]], [[bip-0049.mediawiki|49]], and [[bip-0084.mediawiki|84]],
but with a different purpose value for the script type.

<pre>
m / purpose' / coin_type' / account' / change / address_index
</pre>

For the <tt>purpose</tt>-path level it uses <tt>86'</tt>.
The rest of the levels are used as defined in BIPs 44, 49, and 84.

A key derived with this derivation path pattern will be referred to as <tt>derived_key</tt> further
in this document.

===Address derivation===


[[bip-0341.mediawiki#cite_ref-22-0|BIP 341]] states: "If the spending conditions do not require a
script path, the output key should commit to an unspendable script path instead of having no
script path. This can be achieved by computing the output key point as
''Q = P + int(hash<sub>TapTweak</sub>(bytes(P)))G''." Thus:

<pre>
internal_key:       lift_x(derived_key)
32_byte_output_key: internal_key + int(HashTapTweak(bytes(internal_key)))G
</pre>

In a transaction, the scripts and witnesses are as defined in
[[bip-0341.mediawiki#specification|BIP 341]]:

<pre>
witness:      <signature>
scriptSig:    (empty)
scriptPubKey: 1 <32_byte_output_key>
              (0x5120{32_byte_output_key})
</pre>

==Backwards Compatibility==

This BIP is not backwards compatible by design.
An incompatible wallet will not discover these accounts at all and the user will notice that
something is wrong.

However this BIP uses the same method used in BIPs 44, 49, and 84, so it should not be difficult
to implement.

==Test vectors==

<pre>
mnemonic = abandon abandon abandon abandon abandon abandon abandon abandon abandon abandon abandon about
rootpriv = xprv9s21ZrQH143K3GJpoapnV8SFfukcVBSfeCficPSGfubmSFDxo1kuHnLisriDvSnRRuL2Qrg5ggqHKNVpxR86QEC8w35uxmGoggxtQTPvfUu
rootpub  = xpub661MyMwAqRbcFkPHucMnrGNzDwb6teAX1RbKQmqtEF8kK3Z7LZ59qafCjB9eCRLiTVG3uxBxgKvRgbubRhqSKXnGGb1aoaqLrpMBDrVxga8

// Account 0, root = m/86'/0'/0'
xprv = xprv9xgqHN7yz9MwCkxsBPN5qetuNdQSUttZNKw1dcYTV4mkaAFiBVGQziHs3NRSWMkCzvgjEe3n9xV8oYywvM8at9yRqyaZVz6TYYhX98VjsUk
xpub = xpub6BgBgsespWvERF3LHQu6CnqdvfEvtMcQjYrcRzx53QJjSxarj2afYWcLteoGVky7D3UKDP9QyrLprQ3VCECoY49yfdDEHGCtMMj92pReUsQ

// Account 0, first receiving address = m/86'/0'/0'/0/0
xprv         = xprvA449goEeU9okwCzzZaxiy475EQGQzBkc65su82nXEvcwzfSskb2hAt2WymrjyRL6kpbVTGL3cKtp9herYXSjjQ1j4stsXXiRF7kXkCacK3T
xpub         = xpub6H3W6JmYJXN49h5TfcVjLC3onS6uPeUTTJoVvRC8oG9vsTn2J8LwigLzq5tHbrwAzH9DGo6ThGUdWsqce8dGfwHVBxSbixjDADGGdzF7t2B
internal_key = cc8a4bc64d897bddc5fbc2f670f7a8ba0b386779106cf1223c6fc5d7cd6fc115
output_key   = a60869f0dbcf1dc659c9cecbaf8050135ea9e8cdc487053f1dc6880949dc684c
scriptPubKey = 5120a60869f0dbcf1dc659c9cecbaf8050135ea9e8cdc487053f1dc6880949dc684c
address      = bc1p5cyxnuxmeuwuvkwfem96lqzszd02n6xdcjrs20cac6yqjjwudpxqkedrcr

// Account 0, second receiving address = m/86'/0'/0'/0/1
xprv         = xprvA449goEeU9okyiF1LmKiDaTgeXvmh87DVyRd35VPbsSop8n8uALpbtrUhUXByPFKK7C2yuqrB1FrhiDkEMC4RGmA5KTwsE1aB5jRu9zHsuQ
xpub         = xpub6H3W6JmYJXN4CCKUSnriaiQRCZmG6aq4sCMDqTu1ACyngw7HShf59hAxYjXgKDuuHThVEUzdHrc3aXCr9kfvQvZPit5dnD3K9xVRBzjK3rX
internal_key = 83dfe85a3151d2517290da461fe2815591ef69f2b18a2ce63f01697a8b313145
output_key   = a82f29944d65b86ae6b5e5cc75e294ead6c59391a1edc5e016e3498c67fc7bbb
scriptPubKey = 5120a82f29944d65b86ae6b5e5cc75e294ead6c59391a1edc5e016e3498c67fc7bbb
address      = bc1p4qhjn9zdvkux4e44uhx8tc55attvtyu358kutcqkudyccelu0was9fqzwh

// Account 0, first change address = m/86'/0'/0'/1/0
xprv         = xprvA3Ln3Gt3aphvUgzgEDT8vE2cYqb4PjFfpmbiFKphxLg1FjXQpkAk5M1ZKDY15bmCAHA35jTiawbFuwGtbDZogKF1WfjwxML4gK7WfYW5JRP
xpub         = xpub6GL8SnQwRCGDhB59LEz9HMyM6sRYoByXBzXK3iEKWgCz8XrZNHUzd9L3AUBELW5NzA7dEFvMas1F84TuPH3xqdUA5tumaGWFgihJzWytXe3
internal_key = 399f1b2f4393f29a18c937859c5dd8a77350103157eb880f02e8c08214277cef
output_key   = 882d74e5d0572d5a816cef0041a96b6c1de832f6f9676d9605c44d5e9a97d3dc
scriptPubKey = 5120882d74e5d0572d5a816cef0041a96b6c1de832f6f9676d9605c44d5e9a97d3dc
address      = bc1p3qkhfews2uk44qtvauqyr2ttdsw7svhkl9nkm9s9c3x4ax5h60wqwruhk7
</pre>

==Reference==

* [[bip-0032.mediawiki|BIP32 - Hierarchical Deterministic Wallets]]
* [[bip-0043.mediawiki|BIP43 - Purpose Field for Deterministic Wallets]]
* [[bip-0044.mediawiki|BIP44 - Multi-Account Hierarchy for Deterministic Wallets]]
* [[bip-0049.mediawiki|BIP49 - Derivation scheme for P2WPKH-nested-in-P2SH based accounts]]
* [[bip-0084.mediawiki|BIP84 - Derivation scheme for P2WPKH based accounts]]
* [[bip-0341.mediawiki|BIP341 - Taproot: SegWit version 1 spending rules]]
