(16 Apr 2013) Added private derivation for i ≥ 0x80000000 (less risk of parent private key leakage)
(30 Apr 2013) Switched from multiplication by IL to addition of IL (faster, easier implementation)
(25 May 2013) Added test vectors
(15 Jan 2014) Rename keys with index ≥ 0x80000000 to hardened keys, and add explicit conversion functions.
(24 Feb 2017) Added test vectors for hardened derivation with leading zeros
Title: Hierarchical Deterministic Wallets
Author: Pieter WuilleComments-Summary: No comments yet.
This document describes hierarchical deterministic wallets (or “HD Wallets”): wallets which can be shared partially or entirely with different systems, each with or without the ability to spend coins.
The specification is intended to set a standard for deterministic wallets that can be interchanged between different clients. Although the wallets described here have many features, not all are required by supporting clients.
The specification consists of two parts. In the first part, a system for deriving a tree of keypairs from a single seed is presented. The second part demonstrates how to build a wallet structure on top of such a tree.
This BIP is licensed under the 2-clause BSD license.
The Bitcoin reference client uses randomly generated keys. In order to avoid the necessity for a backup after every transaction, (by default) 100 keys are cached in a pool of reserve keys. Still, these wallets are not intended to be shared and used on several systems simultaneously. They support hiding their private keys by using the wallet encrypt feature and not sharing the password, but such “neutered” wallets lose the power to generate public keys as well.
Deterministic wallets do not require such frequent backups, and elliptic curve mathematics permit schemes where one can calculate the public keys without revealing the private keys. This permits, for example, a webshop business to let its webserver generate fresh addresses (public key hashes) for each order or for each customer, without giving the webserver access to the corresponding private keys (which are required for spending the received funds).
However, deterministic wallets typically consist of a single “chain” of keypairs. The fact that there is only one chain means that sharing a wallet happens on an all-or-nothing basis. However, in some cases one only wants some (public) keys to be shared and recoverable. In the example of a webshop, the webserver does not need access to all public keys of the merchant’s wallet; only to those addresses which are used to receive customer’s payments, and not for example the change addresses that are generated when the merchant spends money. Hierarchical deterministic wallets allow such selective sharing by supporting multiple keypair chains, derived from a single root.
Specification: Key derivation
In the rest of this text we will assume the public key cryptography used in Bitcoin, namely elliptic curve cryptography using the field and curve parameters defined by secp256k1 (https://www.secg.org/sec2-v2.pdf). Variables below are either:
Addition (+) of two coordinate pair is defined as application of the EC group operation.
Concatenation (||) is the operation of appending one byte sequence onto another.
As standard conversion functions, we assume:
point(p): returns the coordinate pair resulting from EC point multiplication (repeated application of the EC group operation) of the secp256k1 base point with the integer p.
ser32(i): serialize a 32-bit unsigned integer i as a 4-byte sequence, most significant byte first.
ser256(p): serializes the integer p as a 32-byte sequence, most significant byte first.
serP(P): serializes the coordinate pair P = (x,y) as a byte sequence using SEC1’s compressed form: (0x02 or 0x03) || ser256(x), where the essay-header byte depends on the parity of the omitted y coordinate.
parse256(p): interprets a 32-byte sequence as a 256-bit number, most significant byte first.
In what follows, we will define a function that derives a number of child keys from a parent key. In order to prevent these from depending solely on the key itself, we extend both private and public keys first with an extra 256 bits of entropy. This extension, called the chain code, is identical for corresponding private and public keys, and consists of 32 bytes.
We represent an extended private key as (k, c), with k the normal private key, and c the chain code. An extended public key is represented as (K, c), with K = point(k) and c the chain code.
Each extended key has 231 normal child keys, and 231 hardened child keys. Each of these child keys has an index. The normal child keys use indices 0 through 231-1. The hardened child keys use indices 231 through 232-1. To ease notation for hardened key indices, a number iH represents i+231.
=Child key derivation (CKD) functions=
Given a parent extended key and an index i, it is possible to compute the corresponding child extended key. The algorithm to do so depends on whether the child is a hardened key or not (or, equivalently, whether i ≥ 231), and whether we’re talking about private or public keys.
==Private parent key → private child key==
The function CKDpriv((kpar, cpar), i) → (ki, ci) computes a child extended private key from the parent extended private key:
这里(kpar, cpar)是扩展父私钥，其中kpar是父私钥， cpar是链码; i是子密钥序号，(ki, ci)是对应的第i个扩展子私钥
Check whether i ≥ 231 (whether the child is a hardened key).
If so (hardened child): let I = HMAC-SHA512(Key = cpar, Data = 0x00 || ser256(kpar) || ser32(i)). (Note: The 0x00 pads the private key to make it 33 bytes long.) If not (normal child): let I = HMAC-SHA512(Key = cpar, Data = serP(point(kpar)) || ser32(i)).
Split I into two 32-byte sequences, IL and IR.
The returned child key ki is parse256(IL) + kpar (mod n).
The returned chain code ci is IR.
In case parse256(IL) ≥ n or ki = 0, the resulting key is invalid, and one should proceed with the next value for i. (Note: this has probability lower than 1 in 2127.)
The HMAC-SHA512 function is specified in [https://tools.ietf.org/html/rfc4231 RFC 4231].
==Public parent key → public child key==
The function CKDpub((Kpar, cpar), i) → (Ki, ci) computes a child extended public key from the parent extended public key. It is only defined for non-hardened child keys.
Check whether i ≥ 231 (whether the child is a hardened key).
If so (hardened child): return failure If not (normal child): let I = HMAC-SHA512(Key = cpar, Data = serP(Kpar) || ser32(i)).
我们可以比较父私钥——>子私钥推导算法中的核心函数I = HMAC-SHA512(Key = cpar, Data = serP(point(kpar)) || ser32(i))和父公钥——>子公钥推导算法中的核心函数I = HMAC-SHA512(Key = cpar, Data = serP(Kpar) || ser32(i))，可以看到后者中的Kpar（即父公钥）就是前者中的point(kpar)（从父私钥计算得到的父公钥），即两个函数本质是一模一样的
Split I into two 32-byte sequences, IL and IR.
The returned child key Ki is
point(parse256(IL)) + Kpar.
需要注意：point(parse256(IL)) + Kpar中的加法不是数字之间的加法，而是椭圆曲线上点的加法。
特别说明:对于普通子密钥，由父公钥计算得到的子公钥与由对应的父私钥计算得到的子私钥是对应成对的。这是因为point(parse256(IL) + kpar)=(parse256(IL) + kpar)∗G=parse256(IL)∗G+kpar∗G=point(parse256(IL)) + Kpar=Ki.即从父私钥推导出的子私钥计算得到的相应的子公钥等于由父公钥直接推导出的子公钥
The returned chain code ci is IR.
In case parse256(IL) ≥ n or Ki is the point at infinity, the resulting key is invalid, and one should proceed with the next value for i.
==Private parent key → public child key==
The function N((k, c)) → (K, c) computes the extended public key corresponding to an extended private key (the “neutered” version, as it removes the ability to sign transactions).
To compute the public child key of a parent private key:
N(CKDpriv((kpar, cpar), i)) (works always).
CKDpub(N(kpar, cpar), i) (works only for non-hardened child keys).
The fact that they are equivalent is what makes non-hardened keys useful (one can derive child public keys of a given parent key without knowing any private key), and also what distinguishes them from hardened keys. The reason for not always using non-hardened keys (which are more useful) is security; see further for more information.
==Public parent key → private child key==
This is not possible.
=The key tree=
The next step is cascading several CKD constructions to build a tree. We start with one root, the master extended key m. By evaluating CKDpriv(m,i) for several values of i, we get a number of level-1 derived nodes. As each of these is again an extended key, CKDpriv can be applied to those as well.
To shorten notation, we will write CKDpriv(CKDpriv(CKDpriv(m,3H),2),5) as m/3H/2/5. Equivalently for public keys, we write CKDpub(CKDpub(CKDpub(M,3),2),5) as M/3/2/5. This results in the following identities:
N(m/a/b/c) = N(m/a/b)/c = N(m/a)/b/c = N(m)/a/b/c = M/a/b/c.
N(m/aH/b/c) = N(m/aH/b)/c
However, N(m/aH) cannot be rewritten as N(m)/aH, as the latter is not possible.
Each leaf node in the tree corresponds to an actual key, while the internal nodes correspond to the collections of keys that descend from them. The chain codes of the leaf nodes are ignored, and only their embedded private or public key is relevant. Because of this construction, knowing an extended private key allows reconstruction of all descendant private keys and public keys, and knowing an extended public keys allows reconstruction of all descendant non-hardened public keys.
Extended keys can be identified by the Hash160 (RIPEMD160 after SHA256) of the serialized ECDSA public key K, ignoring the chain code. This corresponds exactly to the data used in traditional Bitcoin addresses. It is not advised to represent this data in base58 format though, as it may be interpreted as an address that way (and wallet software is not required to accept payment to the chain key itself).
The first 32 bits of the identifier are called the key fingerprint.
Extended public and private keys are serialized as follows:
version bytes (mainnet: 0x0488B21E public, 0x0488ADE4 private;
testnet: 0x043587CF public, 0x04358394 private)
1 byte: depth: 0x00 for master nodes, 0x01 for level-1 derived keys, ….
4 bytes: the fingerprint of the parent’s key (0x00000000 if master key)
4 bytes: child number. This is ser32(i) for i in xi = xpar/i, with xi the key being serialized. (0x00000000 if master key)
32 bytes: the chain code
33 bytes: the public key or private key data (serP(K) for public keys, 0x00 || ser256(k) for private keys)
This 78 byte structure can be encoded like other Bitcoin data in Base58, by first adding 32 checksum bits (derived from the double SHA-256 checksum), and then converting to the Base58 representation. This results in a Base58-encoded string of up to 112 characters. Because of the choice of the version bytes, the Base58 representation will start with “xprv” or “xpub” on mainnet, “tprv” or “tpub” on testnet.
Note that the fingerprint of the parent only serves as a fast way to detect parent and child nodes in software, and software must be willing to deal with collisions. Internally, the full 160-bit identifier could be used.
When importing a serialized extended public key, implementations must verify whether the X coordinate in the public key data corresponds to a point on the curve. If not, the extended public key is invalid.
=Master key generation=
The total number of possible extended keypairs is almost 2512, but the produced keys are only 256 bits long, and offer about half of that in terms of security. Therefore, master keys are not generated directly, but instead from a potentially short seed value.
Generate a seed byte sequence S of a chosen length (between 128 and 512 bits; 256 bits is advised) from a (P)RNG.
Calculate I = HMAC-SHA512(Key = “Bitcoin seed”, Data = S)
Split I into two 32-byte sequences, IL and IR.
Use parse256(IL) as master secret key, and IR as master chain code.
In case IL is 0 or ≥n, the master key is invalid.
Specification: Wallet structure
The previous sections specified key trees and their nodes. The next step is imposing a wallet structure on this tree. The layout defined in this section is a default only, though clients are encouraged to mimic it for compatibility, even if not all features are supported.
=The default wallet layout=
An HDW is organized as several ‘accounts’. Accounts are numbered, the default account ("") being number 0. Clients are not required to support more than one account - if not, they only use the default account.
Each account is composed of two keypair chains: an internal and an external one. The external keychain is used to generate new public addresses, while the internal keychain is used for all other operations (change addresses, generation addresses, …, anything that doesn’t need to be communicated). Clients that do not support separate keychains for these should use the external one for everything.
m/iH/0/k corresponds to the k’th keypair of the external chain of account number i of the HDW derived from master m.
m/iH/1/k corresponds to the k’th keypair of the internal chain of account number i of the HDW derived from master m.
==Full wallet sharing: m==
In cases where two systems need to access a single shared wallet, and both need to be able to perform spendings, one needs to share the master private extended key. Nodes can keep a pool of N look-ahead keys cached for external chains, to watch for incoming payments. The look-ahead for internal chains can be very small, as no gaps are to be expected here. An extra look-ahead could be active for the first unused account’s chains - triggering the creation of a new account when used. Note that the name of the account will still need to be entered manually and cannot be synchronized via the block chain.
In case an auditor needs full access to the list of incoming and outgoing payments, one can share all account public extended keys. This will allow the auditor to see all transactions from and to the wallet, in all accounts, but not a single secret key.
==Per-office balances: m/iH==
When a business has several independent offices, they can all use wallets derived from a single master. This will allow the headquarters to maintain a super-wallet that sees all incoming and outgoing transactions of all offices, and even permit moving money between the offices.
==Recurrent business-to-business transactions: N(m/iH/0)==
In case two business partners often transfer money, one can use the extended public key for the external chain of a specific account (M/i h/0) as a sort of “super address”, allowing frequent transactions that cannot (easily) be associated, but without needing to request a new address for each payment.
Such a mechanism could also be used by mining pool operators as variable payout address.
==Unsecure money receiver: N(m/iH/0)==
When an unsecure webserver is used to run an e-commerce site, it needs to know public addresses that are used to receive payments. The webserver only needs to know the public extended key of the external chain of a single account. This means someone illegally obtaining access to the webserver can at most see all incoming payments but will not be able to steal the money, will not (trivially) be able to distinguish outgoing transactions, nor be able to see payments received by other webservers if there are several.
To comply with this standard, a client must at least be able to import an extended public or private key, to give access to its direct descendants as wallet keys. The wallet structure (master/account/chain/subchain) presented in the second part of the specification is advisory only, but is suggested as a minimal structure for easy compatibility - even when no separate accounts or distinction between internal and external chains is made. However, implementations may deviate from it for specific needs; more complex applications may call for a more complex tree structure.
In addition to the expectations from the EC public-key cryptography itself:
Given a public key K, an attacker cannot find the corresponding private key more efficiently than by solving the EC discrete logarithm problem (assumed to require 2128 group operations).
the intended security properties of this standard are:
Given a child extended private key (ki,ci) and the integer i, an attacker cannot find the parent private key kpar more efficiently than a 2256 brute force of HMAC-SHA512.
Given any number (2 ≤ N ≤ 232-1) of (index, extended private key) tuples (ij,(kij,cij)), with distinct ij‘s, determining whether they are derived from a common parent extended private key (i.e., whether there exists a (kpar,cpar) such that for each j in (0..N-1) CKDpriv((kpar,cpar),ij)=(kij,cij)), cannot be done more efficiently than a 2256 brute force of HMAC-SHA512.
Note however that the following properties does not exist:
Given a parent extended public key (Kpar,cpar) and a child public key (Ki), it is hard to find i.
Given a parent extended public key (Kpar,cpar) and a non-hardened child private key (ki), it is hard to find kpar.
Private and public keys must be kept safe as usual. Leaking a private key means access to coins - leaking a public key can mean loss of privacy.
Somewhat more care must be taken regarding extended keys, as these correspond to an entire (sub)tree of keys.
One weakness that may not be immediately obvious, is that knowledge of a parent extended public key plus any non-hardened private key descending from it is equivalent to knowing the parent extended private key (and thus every private and public key descending from it). This means that extended public keys must be treated more carefully than regular public keys.
It is also the reason for the existence of hardened keys, and why they are used for the account level in the tree. This way, a leak of account-specific (or below) private key never risks compromising the master or other accounts.
=Test vector 1=
Seed (hex): 000102030405060708090a0b0c0d0e0f
ext prv: xprv9s21ZrQH143K3QTDL4LXw2F7HEK3wJUD2nW2nRk4stbPy6cq3jPPqjiChkVvvNKmPGJxWUtg6LnF5kejMRNNU3TGtRBeJgk33yuGBxrMPHi
ext prv: xprv9uHRZZhk6KAJC1avXpDAp4MDc3sQKNxDiPvvkX8Br5ngLNv1TxvUxt4cV1rGL5hj6KCesnDYUhd7oWgT11eZG7XnxHrnYeSvkzY7d2bhkJ7
ext prv: xprv9wTYmMFdV23N2TdNG573QoEsfRrWKQgWeibmLntzniatZvR9BmLnvSxqu53Kw1UmYPxLgboyZQaXwTCg8MSY3H2EU4pWcQDnRnrVA1xe8fs
ext prv: xprv9z4pot5VBttmtdRTWfWQmoH1taj2axGVzFqSb8C9xaxKymcFzXBDptWmT7FwuEzG3ryjH4ktypQSAewRiNMjANTtpgP4mLTj34bhnZX7UiM
=Test vector 2=
Seed (hex): fffcf9f6f3f0edeae7e4e1dedbd8d5d2cfccc9c6c3c0bdbab7b4b1aeaba8a5a29f9c999693908d8a8784817e7b7875726f6c696663605d5a5754514e4b484542
ext pub: xpub661MyMwAqRbcFW31YEwpkMuc5THy2PSt5bDMsktWQcFF8syAmRUapSCGu8ED9W6oDMSgv6Zz8idoc4a6mr8BDzTJY47LJhkJ8UB7WEGuduB
ext pub: xpub69H7F5d8KSRgmmdJg2KhpAK8SR3DjMwAdkxj3ZuxV27CprR9LgpeyGmXUbC6wb7ERfvrnKZjXoUmmDznezpbZb7ap6r1D3tgFxHmwMkQTPH
ext prv: xprv9vHkqa6EV4sPZHYqZznhT2NPtPCjKuDKGY38FBWLvgaDx45zo9WQRUT3dKYnjwih2yJD9mkrocEZXo1ex8G81dwSM1fwqWpWkeS3v86pgKt
ext prv: xprv9wSp6B7kry3Vj9m1zSnLvN3xH8RdsPP1Mh7fAaR7aRLcQMKTR2vidYEeEg2mUCTAwCd6vnxVrcjfy2kRgVsFawNzmjuHc2YmYRmagcEPdU9
extpub:xpub6DF8uhdarytz3FWdA8TvFSvvAh8dP3283MY7p2V4SeE2wyWmG5mg5EwVvmdMVCQcoNJxGoWaU9DCWh89LojfZ537wTfunKau47EL2dhHKon ext prv: xprv9zFnWC6h2cLgpmSA46vutJzBcfJ8yaJGg8cX1e5StJh45BBciYTRXSd25UEPVuesF9yog62tGAQtHjXajPPdbRCHuWS6T8XA2ECKADdw4Ef
ext prv: xprvA1RpRA33e1JQ7ifknakTFpgNXPmW2YvmhqLQYMmrj4xJXXWYpDPS3xz7iAxn8L39njGVyuoseXzU6rcxFLJ8HFsTjSyQbLYnMpCqE2VbFWc
ext prv: xprvA2nrNbFZABcdryreWet9Ea4LvTJcGsqrMzxHx98MMrotbir7yrKCEXw7nadnHM8Dq38EGfSh6dqA9QWTyefMLEcBYJUuekgW4BYPJcr9E7j
=Test vector 3=
These vectors test for the retention of leading zeros.
See [https://github.com/bitpay/bitcore-lib/issues/47 bitpay/bitcore-lib#47]
and [https://github.com/iancoleman/bip39/issues/58 iancoleman/bip39#58]
for more information.
ext pub: xpub661MyMwAqRbcEZVB4dScxMAdx6d4nFc9nvyvH3v4gJL378CSRZiYmhRoP7mBy6gSPSCYk6SzXPTf3ND1cZAceL7SfJ1Z3GC8vBgp2epUt13
ext prv: xprv9s21ZrQH143K25QhxbucbDDuQ4naNntJRi4KUfWT7xo4EKsHt2QJDu7KXp1A3u7Bi1j8ph3EGsZ9Xvz9dGuVrtHHs7pXeTzjuxBrCmmhgC6
ext pub: xpub68NZiKmJWnxxS6aaHmn81bvJeTESw724CRDs6HbuccFQN9Ku14VQrADWgqbhhTHBaohPX4CjNLf9fq9MYo6oDaPPLPxSb7gwQN3ih19Zm4Y
ext prv: xprv9uPDJpEQgRQfDcW7BkF7eTya6RPxXeJCqCJGHuCJ4GiRVLzkTXBAJMu2qaMWPrS7AANYqdq6vcBcBUdJCVVFceUvJFjaPdGZ2y9WACViL4L
Two Python implementations exist:
PyCoin (https://github.com/richardkiss/pycoin) is a suite of utilities for dealing with Bitcoin that includes BIP0032 wallet features. BIP32Utils (https://github.com/jmcorgan/bip32utils) is a library and command line interface specifically focused on BIP0032 wallets and scripting.
2 Java implementations exist:
A C++ implementation is available at
An Objective-C implementation is available at
A Ruby implementation is available at
Two Go implementations exist: hdkeychain
(https://github.com/conformal/btcutil/tree/master/hdkeychain) provides an API for bitcoin hierarchical deterministic extended keys (BIP0032). Go HD Wallet (https://github.com/WeMeetAgain/go-hdwallet).
https://github.com/sarchar/brainwallet.github.com/tree/bip32 and https://github.com/bitpay/bitcore
A PHP implementation is available at
A C# implementation is available at
https://github.com/NicolasDorier/NBitcoin (ExtKey, ExtPubKey)
A Haskell implementation is available at
together with a CLI interface at
Gregory Maxwell for the original idea of type-2 deterministic wallets, and many discussions about it.
Alan Reiner for the implementation of this scheme in Armory, and the suggestions that followed from that.
Eric Lombrozo for reviewing and revising this BIP.
Mike Caldwell for the version bytes to obtain human-recognizable Base58 strings.