# BIP 0032

This page describes a BIP (Bitcoin Improvement Proposal). |

BIP: 32 Title: Hierarchical Deterministic Wallets Author: Pieter Wuille Status: Draft Type: Informational Created: 11-02-2012

## Contents

## Abstract

This document describes hierarchical determinstic 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.

## Motivation

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 a 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

### Conventions

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 (http://www.secg.org/index.php?action=secg,docs_secg). Variables below are either:

- integers modulo the order of the curve, serialized as 32 bytes, most significant byte first.
- coordinates of points on the curve, serialized as specified in SEC1: either compressed ([0x02 or 0x03] + 32 byte x coordinate), or uncompressed (0x04 + 32 byte x coordinate + 32 byte y coordinate).
- byte sequences

Addition (+) of two coordinates is defined as application of the EC group operation. Multiplication (*) of an integer and a coordinate is defined as repeated application of the EC group operation. The generator element of the curve is called G. The public key K corresponding to the private key k is calculated as k*G. We do not distinguish between numbers or coordinates and their serialization as byte sequences.

### Extended keys

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 the normal public key and c the chain code.

### Child key derivation function

We define the child key derivation function CKD((k_par,c_par),n), which takes a parent extended secret key (k_par,c_par) and a 32-bit integer n, to produce a child extended secret key (k_n,c_n).

To define (k_n,c_n) = CKD((k_par,c_par),n):

- call I = HMAC-SHA512(Key=c_par, Data=k_par*G || n), where k_par*G is the public key corresponding to k_par, || is concatenation, and n is encoded as a 32 bits unsigned integer, most significant byte first.
- Split I into two 32-byte sequences, I_l and I_r.
- k_n is equal to I_l*k_par.
- c_n is equal to I_r.

We also define a version that operates on extended public keys instead of private ones: (K_n,c_n) = CKD'((K_par,c_par),n):

- call I = HMAC-SHA512(Key=c_par, Data=K_par || n), where n is encoded a 32 bits unsigned integer, most significant byte first.
- Split I into two 32-byte sequences, I_l and I_r.
- K_n is equal to I_l*K_par.
- c_n is equal to I_r.

Note that the extended public key corresponding to the evaluation of CKD(x,n) is identical to the evaluation of CKD'(X,n), with X the extended public key corresponding to x. Symbolically, CKD(x,n)*G = CKD'(x*G,n). This implies that CKD' can be used to derive all public keys corresponding to the private keys that CKD would find. It cannot be used to retrieve the private keys, however.

The HMAC-SHA512 function is specified in RFC 4231.

### 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 CKD(m,n) for several values of n, we get a number of first-degree derivative nodes. As each of these is again an extended key, CKD can be applied to those as well. To shorten notation, we will write CKD(CKD(CKD(m,n_1),n_2),n_3) as m/n_1/n_2/n_3 now.

Each leaf node in the tree corresponds to an actual keypair, while the internal nodes correspond to the collection of keypairs that descends from them. The chain codes of the leaf nodes are ignored, and only their embedded private or public key is used. 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 public keys.

### Serialization format

Extended public and private keys are serialized as follows:

- 1 byte: version byte (mainnet: 0x06 public, 0x0C private; testnet: 0xC6 public, 0xCC private)
- 1 byte: depth: 0x00 for master nodes, 0x01 for level-1 descendants, ....
- 4 bytes: the first 32 bits of RIPEMD160(SHA256(K_par)), a "fingerprint" of the parent's key. Note that this corresponds to the first 32 bits of the data in the "address" corresponding to the parent's key.
- 4 bytes: child number. This is the number n in x_n = x_par/n, with x_n the key being serialized. This is encoded in MSB order.
- 32 bytes: the chain code
- the rest: the normal public or private key serialization (65 or 33 bytes for public keys, 32 or 33 bytes for private keys).

This 74, 75 or 107 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 107, 108 or 152 characters.

### Wallet structure

The previous sections specified key trees and their nodes. The next step is imposing a wallet structure on this tree.

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/i/0/k corresponds to the k'th keypair of the external chain of account number i of the HDW derived from master m. * m/i/1/k corresponds to the k'th keypair of the internal chain of account number i of the HDW derived from master m.

### Master key generation

The total number of possible extended keypairs is almost 2^512, 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 S of a chosen length (at least 128 bits) from a (P)RNG.
- Calculate I = HMAC-SHA512(key="Bitcoin seed", msg=S)
- Split I into two 32-byte sequences, I_l and I_r.
- Use I_l as master secret key, and I_r as master chain code.

## Use cases

### 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.

### Audits: M

In case an auditor needs full access to the list of incoming and outgoing payments, one can share the master public extended key. 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/i

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.

### Recurrant business-to-business transactions: M/i/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/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: M/i/0

When an unsecure webserver is used to run an e-commerce site, it needs to know public addresses that be 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 (trivially) be able to distinguish outgoing transactions, nor see payments received by other webservers if there are several ones.

## Compatibility

## Test Vectors

## Acknowledgements

- 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.