BIP 0085

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  BIP: 85
  Layer: Applications
  Title: Deterministic Entropy From BIP32 Keychains
  Author: Ethan Kosakovsky <ethankosakovsky@protonmail.com>
  Comments-Summary: No comments yet.
  Comments-URI: https://github.com/bitcoin/bips/wiki/Comments:BIP-0085
  Status: Draft
  Type: Informational
  Created: 2020-03-20
  License: BSD-2-Clause
           OPL

Abstract

"One Seed to rule them all, One Key to find them, One Path to bring them all, And in cryptography bind them."

It is not possible to maintain one single (mnemonic) seed backup for all keychains used across various wallets because there are a variety of incompatible standards. Sharing of seeds across multiple wallets is not desirable for security reasons. Physical storage of multiple seeds is difficult depending on the security and redundancy required.

As HD keychains are essentially derived from initial entropy, this proposal provides a way to derive entropy from the keychain which can be fed into whatever method a wallet uses to derive the initial mnemonic seed or root key.

Definitions

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119.

The terminology related to keychains used in the wild varies widely, for example `seed` has various different meanings. In this document we define the terms

1. BIP32 root key is the root extended private key that is represented as the top root of the keychain in BIP32.
2. BIP39 mnemonic is the mnemonic phrase that is calculated from the entropy used before hashing of the mnemonic in BIP39.
3. BIP39 seed is the result of hashing the BIP39 mnemonic seed.

Motivation

Most wallets implement BIP32 which defines how a BIP32 root key can be used to derive keychains. As a consequence, a backup of just the BIP32 root key is sufficient to include all keys derived from it. BIP32 does not have a human friendly serialization of the BIP32 root key (or BIP32 extended keys in general) which makes paper backups or manually restoring the key more error-prone. BIP39 was designed to solve this problem but rather than serialize the BIP32 root key, it takes some entropy, encoded to a "seed mnemonic", which is then hashed to derive the BIP39 seed which can be turned into the BIP32 root key. Saving the BIP39 mnemonic is enough to reconstruct the entire BIP32 keychain, but a BIP32 root key cannot be reversed back to the BIP39 mnemonic.

Most wallets implement BIP39, so on initialization or restoration, the user must interact with a BIP39 mnemonic. Most wallets do not support BIP32 extended private keys, so each wallet must either share the same BIP39 mnemonic, or have a separate BIP39 mnemonic entirely. Neither scenarios are particularly satisfactory for security reasons. For example, some wallets may be inherently less secure like hot wallets on smartphones, Join Market servers, or Lightning Network nodes. Having multiple seeds is far from desirable, especially for those who rely on split key or redundancy backups in different geological locations. Adding is necessarily difficult and may result in users being more lazy with subsequent keys, resulting in compromised security or loss of keys.

There is added complication with wallets that implement other standards, or no standards at all. Bitcoin Core wallet uses a WIF as the hdseed, and yet other wallets like Electrum use different mnemonic schemes to derive the BIP32 root key. Other cryptocurrencies like Monero also use an entirely different mnemonic scheme.

Ultimately, all of the mnemonic/seed schemes start with some "initial entropy" to derive a mnemonic/seed, and then process the mnemonic into a BIP32 key, or private key. We can use BIP32 itself to derive the "initial entropy" to then recreate the same mnemonic or seed according to the specific application standard of the target wallet. We can use a BIP44-like categorization to ensure uniform derivation according to the target application type.

Specification

We assume a single BIP32 master root key. This specification is not concerned with how this was derived (e.g. directly or via a mnemonic scheme such as BIP39).

For each application that requires its own wallet, a unique private key is derived from the BIP32 master root key using a fully hardened derivation path. The resulting private key (k) is then processed with HMAC-SHA512, where the key is "bip-entropy-from-k", and the message payload is the private key k: HMAC-SHA512(key="bip-entropy-from-k", msg=k). The result produces 512 bits of entropy. Each application SHOULD use up to the required number of bits necessary for their operation truncating the rest.

The HMAC-SHA512 function is specified in RFC 4231.

Test vectors

Test case 1

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/0'/0'

OUTPUT:

• DERIVED KEY=cca20ccb0e9a90feb0912870c3323b24874b0ca3d8018c4b96d0b97c0e82ded0
• DERIVED ENTROPY=efecfbccffea313214232d29e71563d941229afb4338c21f9517c41aaa0d16f00b83d2a09ef747e7a64e8e2bd5a14869e693da66ce94ac2da570ab7ee48618f7

Test case 2

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/0'/1'

OUTPUT

• DERIVED KEY=503776919131758bb7de7beb6c0ae24894f4ec042c26032890c29359216e21ba
• DERIVED ENTROPY=70c6e3e8ebee8dc4c0dbba66076819bb8c09672527c4277ca8729532ad711872218f826919f6b67218adde99018a6df9095ab2b58d803b5b93ec9802085a690e

BIP85-DRNG

BIP85-DRNG-SHAKE256 is a deterministic random number generator for cryptographic functions that require deterministic outputs, but where the input to that function requires more than the 64 bytes provided by BIP85's HMAC output. BIP85-DRNG-SHAKE256 uses BIP85 to seed a SHAKE256 stream (from the SHA-3 standard). The input must be exactly 64 bytes long (from the BIP85 HMAC output).

RSA key generation is an example of a function that requires orders of magnitude more than 64 bytes of random input. Further, it is not possible to precalculate the amount of random input required until the function has completed.

   drng_reader = BIP85DRNG.new(bip85_entropy)
   rsa_key = RSA.generate_key(4096, drng_reader.read())

Test Vectors

INPUT: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb

• MASTER BIP32 ROOT KEY: m/83696968'/0'/0'

OUTPUT

• DERIVED KEY=cca20ccb0e9a90feb0912870c3323b24874b0ca3d8018c4b96d0b97c0e82ded0
• DERIVED ENTROPY=efecfbccffea313214232d29e71563d941229afb4338c21f9517c41aaa0d16f00b83d2a09ef747e7a64e8e2bd5a14869e693da66ce94ac2da570ab7ee48618f7

• DRNG(80 bytes)=b78b1ee6b345eae6836c2d53d33c64cdaf9a696487be81b03e822dc84b3f1cd883d7559e53d175f243e4c349e822a957bbff9224bc5dde9492ef54e8a439f6bc8c7355b87a925a37ee405a7502991111

Reference Implementation

• Python library implementation: [1]
• JavaScript library implementation: [2]

Other Implementations

• JavaScript library implementation: [3]

• Coldcard Firmware: [4]

• Ian Coleman's Mnemonic Code Converter: [5] and [6]

• AirGap Vault: [7]

• btc_hd_wallet: [8]

Applications

The Application number defines how entropy will be used post processing. Some basic examples follow:

Derivation path uses the format m/83696968'/{app_no}'/{index}' where {app_no} is the path for the application, and {index} is the index.

BIP39

Application number: 39'

Truncate trailing (least significant) bytes of the entropy to the number of bits required to map to the relevant word length: 128 bits for 12 words, 256 bits for 24 words.

The derivation path format is: m/83696968'/39'/{language}'/{words}'/{index}'

Example: a BIP39 mnemonic with 12 English words (first index) would have the path m/83696968'/39'/0'/12'/0', the next key would be m/83696968'/39'/0'/12'/1' etc.

Language Table

Wordlist	Code
English	0'
Japanese	1'
Korean	2'
Spanish	3'
Chinese (Simplified)	4'
Chinese (Traditional)	5'
French	6'
Italian	7'
Czech	8'

Words Table

Words	Entropy	Code
12 words	128 bits	12'
18 words	192 bits	18'
24 words	256 bits	24'

12 English words

BIP39 English 12 word mnemonic seed

128 bits of entropy as input to BIP39 to derive 12 word mnemonic

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/39'/0'/12'/0'

OUTPUT:

• DERIVED ENTROPY=6250b68daf746d12a24d58b4787a714b
• DERIVED BIP39 MNEMONIC=girl mad pet galaxy egg matter matrix prison refuse sense ordinary nose

18 English words

BIP39 English 18 word mnemonic seed

196 bits of entropy as input to BIP39 to derive 18 word mnemonic

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/39'/0'/18'/0'

OUTPUT:

• DERIVED ENTROPY=938033ed8b12698449d4bbca3c853c66b293ea1b1ce9d9dc
• DERIVED BIP39 MNEMONIC=near account window bike charge season chef number sketch tomorrow excuse sniff circle vital hockey outdoor supply token

24 English words

Derives 24 word BIP39 mnemonic seed

256 bits of entropy as input to BIP39 to derive 24 word mnemonic

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/39'/0'/24'/0'

OUTPUT:

• DERIVED ENTROPY=ae131e2312cdc61331542efe0d1077bac5ea803adf24b313a4f0e48e9c51f37f
• DERIVED BIP39 MNEMONIC=puppy ocean match cereal symbol another shed magic wrap hammer bulb intact gadget divorce twin tonight reason outdoor destroy simple truth cigar social volcano

HD-Seed WIF

Application number: 2'

Uses 256 bits[1] of entropy as the secret exponent to derive a private key and encode as a compressed WIF which will be used as the hdseed for Bitcoin Core wallets.

Path format is m/83696968'/2'/{index}'

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/2'/0'

OUTPUT

• DERIVED ENTROPY=7040bb53104f27367f317558e78a994ada7296c6fde36a364e5baf206e502bb1
• DERIVED WIF=Kzyv4uF39d4Jrw2W7UryTHwZr1zQVNk4dAFyqE6BuMrMh1Za7uhp

XPRV

Application number: 32'

Taking 64 bytes of the HMAC digest, the first 32 bytes are the chain code, and second 32 bytes[1] are the private key for BIP32 XPRV value. Child number, depth, and parent fingerprint are forced to zero.

Path format is m/83696968'/32'/{index}'

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/32'/0'

OUTPUT

• DERIVED ENTROPY=ead0b33988a616cf6a497f1c169d9e92562604e38305ccd3fc96f2252c177682
• DERIVED XPRV=xprv9s21ZrQH143K2srSbCSg4m4kLvPMzcWydgmKEnMmoZUurYuBuYG46c6P71UGXMzmriLzCCBvKQWBUv3vPB3m1SATMhp3uEjXHJ42jFg7myX

HEX

Application number: 128169'

The derivation path format is: m/83696968'/128169'/{num_bytes}'/{index}'

`16 <= num_bytes <= 64`

Truncate trailing (least significant) bytes of the entropy after `num_bytes`.

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/128169'/64'/0'

OUTPUT

• DERIVED ENTROPY=492db4698cf3b73a5a24998aa3e9d7fa96275d85724a91e71aa2d645442f878555d078fd1f1f67e368976f04137b1f7a0d19232136ca50c44614af72b5582a5c

PWD BASE64

Application number: 707764'

The derivation path format is: m/83696968'/707764'/{pwd_len}'/{index}'

`20 <= pwd_len <= 86`

Base64 encode the all 64 bytes of entropy. Remove any spaces or new lines inserted by Base64 encoding process. Slice base64 result string on index 0 to `pwd_len`. This slice is the password. As `pwd_len` is limited to 86, passwords will not contain padding.

Entropy calculation:
R = 64 (base64 - do not count padding)
L = pwd_len
Entropy = log2(R ** L)

pwd_length	(cca) entropy
20	120.0
24	144.0
32	192.0
64	384.0
86	516.0

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/707764'/21'/0'

OUTPUT

• DERIVED ENTROPY=d7ad61d4a76575c5bad773feeb40299490b224e8e5df6c8ad8fe3d0a6eed7b85ead9fef7bcca8160f0ee48dc6e92b311fc71f2146623cc6952c03ce82c7b63fe
• DERIVED PWD=dKLoepugzdVJvdL56ogNV

PWD BASE85

Application number: 707785'

The derivation path format is: m/83696968'/707785'/{pwd_len}'/{index}'

`10 <= pwd_len <= 80`

Base85 encode the all 64 bytes of entropy. Remove any spaces or new lines inserted by Base64 encoding process. Slice base85 result string on index 0 to `pwd_len`. This slice is the password. `pwd_len` is limited to 80 characters.

Entropy calculation:
R = 85
L = pwd_len
Entropy = log2(R ** L)

pwd_length	(cca) entropy
10	64.0
15	96.0
20	128.0
30	192.0
80	512.0

INPUT:

• MASTER BIP32 ROOT KEY: xprv9s21ZrQH143K2LBWUUQRFXhucrQqBpKdRRxNVq2zBqsx8HVqFk2uYo8kmbaLLHRdqtQpUm98uKfu3vca1LqdGhUtyoFnCNkfmXRyPXLjbKb
• PATH: m/83696968'/707785'/12'/0'

OUTPUT

• DERIVED ENTROPY=f7cfe56f63dca2490f65fcbf9ee63dcd85d18f751b6b5e1c1b8733af6459c904a75e82b4a22efff9b9e69de2144b293aa8714319a054b6cb55826a8e51425209
• DERIVED PWD=_s`{TW89)i4`

RSA

Application number: 828365'

The derivation path format is: m/83696968'/828365'/{key_bits}'/{key_index}'

The RSA key generator should use BIP85-DRNG as the input RNG function.

RSA GPG

Keys allocated for RSA-GPG purposes use the following scheme:

- Main key m/83696968'/828365'/{key_bits}'/{key_index}'
- Sub keys:  m/83696968'/828365'/{key_bits}'/{key_index}'/{sub_key}'

   - key_index is the parent key for CERTIFY capability
   - sub_key 0' is used as the ENCRYPTION key
   - sub_key 1' is used as the AUTHENTICATION key
   - sub_key 2' is usually used as SIGNATURE key

Note on timestamps:

The resulting RSA key can be used to create a GPG key where the creation date MUST be fixed to unix Epoch timestamp 1231006505 (the Bitcoin genesis block time '2009-01-03 18:05:05' UTC) because the key fingerprint is affected by the creation date (Epoch timestamp 0 was not chosen because of legacy behavior in GNUPG implementations for older keys). Additionally, when importing sub-keys under a key in GNUPG, the system time must be frozen to the same timestamp before importing (e.g. by use of faketime).

Note on GPG key capabilities on smartcard/hardware devices:

GPG capable smart-cards SHOULD be loaded as follows: The encryption slot SHOULD be loaded with the ENCRYPTION capable key; the authentication slot SHOULD be loaded with the AUTHENTICATION capable key. The signature capable slot SHOULD be loaded with the SIGNATURE capable key.

However, depending on available slots on the smart-card, and preferred policy, the CERTIFY capable key MAY be flagged with CERTIFY and SIGNATURE capabilities and loaded into the SIGNATURE capable slot (for example where the smart-card has only three slots and the CERTIFY capability is required on the same card). In this case, the SIGNATURE capable sub-key would be disregarded because the CERTIFY capable key serves a dual purpose.

Backwards Compatibility

This specification is not backwards compatible with any other existing specification.

This specification relies on BIP32 but is agnostic to how the BIP32 root key is derived. As such, this standard is able to derive wallets with initialization schemes like BIP39 or Electrum wallet style mnemonics.

Discussion

The reason for running the derived key through HMAC-SHA512 and truncating the result as necessary is to prevent leakage of the parent tree should the derived key (k) be compromized. While the specification requires the use of hardended key derivation which would prevent this, we cannot enforce hardened derivation, so this method ensures the derived entropy is hardened. Also, from a semantic point of view, since the purpose is to derive entropy and not a private key, we are required to transform the child key. This is done out of an abundance of caution, in order to ward off unwanted side effects should k be used for a dual purpose, including as a nonce hash(k), where undesirable and unforeseen interactions could occur.

Acknowledgements

Many thanks to Peter Gray and Christopher Allen for their input, and to Peter for suggesting extra application use cases.

References

BIP32, BIP39

Footnotes

[1] There is a very small chance that you'll make an invalid key that is zero or bigger than the order of the curve. If this occurs, software should hard fail (forcing users to iterate to the next index).

From BIP32: In case parse₂₅₆(I_L) is 0 or ≥ n, the resulting key is invalid, and one should proceed with the next value for i. (Note: this has probability lower than 1 in 2¹²⁷.)

Copyright

This BIP is dual-licensed under the Open Publication License and BSD 2-clause license.