extendedkey.go

// Copyright (c) 2014-2016 The btcsuite developers
// Use of this source code is governed by an ISC
// license that can be found in the LICENSE file.

package hdkeychain

// References:
//   [BIP32]: BIP0032 - Hierarchical Deterministic Wallets
//   https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki

import (
	"bytes"
	"crypto/hmac"
	"crypto/rand"
	"crypto/sha256"
	"crypto/sha512"
	"encoding/binary"
	"fmt"
	"math/big"

	"github.com/pkt-cash/pktd/btcutil/er"

	"github.com/pkt-cash/pktd/btcec"
	"github.com/pkt-cash/pktd/btcutil"
	"github.com/pkt-cash/pktd/btcutil/base58"
	"github.com/pkt-cash/pktd/chaincfg"
	"github.com/pkt-cash/pktd/chaincfg/chainhash"
)

const (
	// RecommendedSeedLen is the recommended length in bytes for a seed
	// to a master node.
	RecommendedSeedLen = 32 // 256 bits

	// HardenedKeyStart is the index at which a hardended key starts.  Each
	// extended key has 2^31 normal child keys and 2^31 hardned child keys.
	// Thus the range for normal child keys is [0, 2^31 - 1] and the range
	// for hardened child keys is [2^31, 2^32 - 1].
	HardenedKeyStart = 0x80000000 // 2^31

	// MinSeedBytes is the minimum number of bytes allowed for a seed to
	// a master node.
	MinSeedBytes = 16 // 128 bits

	// MaxSeedBytes is the maximum number of bytes allowed for a seed to
	// a master node.
	MaxSeedBytes = 64 // 512 bits

	// serializedKeyLen is the length of a serialized public or private
	// extended key.  It consists of 4 bytes version, 1 byte depth, 4 bytes
	// fingerprint, 4 bytes child number, 32 bytes chain code, and 33 bytes
	// public/private key data.
	serializedKeyLen = 4 + 1 + 4 + 4 + 32 + 33 // 78 bytes

	// maxUint8 is the max positive integer which can be serialized in a uint8
	maxUint8 = 1<<8 - 1
)

// ExtendedKeyErr is a type for the hdkeychain errors
var ExtendedKeyErr er.ErrorType = er.NewErrorType("hdkeychain.ExtendedKeyErr")

var (
	// ErrDeriveHardFromPublic describes an error in which the caller
	// attempted to derive a hardened extended key from a public key.
	ErrDeriveHardFromPublic = ExtendedKeyErr.CodeWithDetail(
		"ErrDeriveHardFromPublic",
		"cannot derive a hardened key from a public key",
	)

	// ErrDeriveBeyondMaxDepth describes an error in which the caller
	// has attempted to derive more than 255 keys from a root key.
	ErrDeriveBeyondMaxDepth = ExtendedKeyErr.CodeWithDetail(
		"ErrDeriveBeyondMaxDepth",
		"cannot derive a key with more than 255 indices in its path",
	)

	// ErrNotPrivExtKey describes an error in which the caller attempted
	// to extract a private key from a public extended key.
	ErrNotPrivExtKey = ExtendedKeyErr.CodeWithDetail(
		"ErrNotPrivExtKey",
		"unable to create private keys from a public extended key",
	)

	// ErrInvalidChild describes an error in which the child at a specific
	// index is invalid due to the derived key falling outside of the valid
	// range for secp256k1 private keys.  This error indicates the caller
	// should simply ignore the invalid child extended key at this index and
	// increment to the next index.
	ErrInvalidChild = ExtendedKeyErr.CodeWithDetail(
		"ErrInvalidChild",
		"the extended key at this index is invalid",
	)

	// ErrUnusableSeed describes an error in which the provided seed is not
	// usable due to the derived key falling outside of the valid range for
	// secp256k1 private keys.  This error indicates the caller must choose
	// another seed.
	ErrUnusableSeed = ExtendedKeyErr.CodeWithDetail("ErrUnusableSeed",
		"unusable seed",
	)

	// ErrInvalidSeedLen describes an error in which the provided seed or
	// seed length is not in the allowed range.
	ErrInvalidSeedLen = ExtendedKeyErr.CodeWithDetail(
		"ErrInvalidSeedLen",
		fmt.Sprintf("seed length must be between %d and %d "+
			"bits", MinSeedBytes*8, MaxSeedBytes*8),
	)

	// ErrBadChecksum describes an error in which the checksum encoded with
	// a serialized extended key does not match the calculated value.
	ErrBadChecksum = ExtendedKeyErr.CodeWithDetail(
		"ErrBadChecksum",
		"bad extended key checksum",
	)

	// ErrInvalidKeyLen describes an error in which the provided serialized
	// key is not the expected length.
	ErrInvalidKeyLen = ExtendedKeyErr.CodeWithDetail(
		"ErrInvalidKeyLen",
		"the provided serialized extended key length is invalid",
	)
)

// masterKey is the master key used along with a random seed used to generate
// the master node in the hierarchical tree.
var masterKey = []byte("Bitcoin seed")

// ExtendedKey houses all the information needed to support a hierarchical
// deterministic extended key.  See the package overview documentation for
// more details on how to use extended keys.
type ExtendedKey struct {
	key       []byte // This will be the pubkey for extended pub keys
	pubKey    []byte // This will only be set for extended priv keys
	chainCode []byte
	depth     uint8
	parentFP  []byte
	childNum  uint32
	version   []byte
	isPrivate bool
}

// NewExtendedKey returns a new instance of an extended key with the given
// fields.  No error checking is performed here as it's only intended to be a
// convenience method used to create a populated struct. This function should
// only by used by applications that need to create custom ExtendedKeys. All
// other applications should just use NewMaster, Derive, or Neuter.
func NewExtendedKey(version, key, chainCode, parentFP []byte, depth uint8,
	childNum uint32, isPrivate bool) *ExtendedKey {

	// NOTE: The pubKey field is intentionally left nil so it is only
	// computed and memoized as required.
	return &ExtendedKey{
		key:       key,
		chainCode: chainCode,
		depth:     depth,
		parentFP:  parentFP,
		childNum:  childNum,
		version:   version,
		isPrivate: isPrivate,
	}
}

// pubKeyBytes returns bytes for the serialized compressed public key associated
// with this extended key in an efficient manner including memoization as
// necessary.
//
// When the extended key is already a public key, the key is simply returned as
// is since it's already in the correct form.  However, when the extended key is
// a private key, the public key will be calculated and memoized so future
// accesses can simply return the cached result.
func (k *ExtendedKey) pubKeyBytes() []byte {
	// Just return the key if it's already an extended public key.
	if !k.isPrivate {
		return k.key
	}

	// This is a private extended key, so calculate and memoize the public
	// key if needed.
	if len(k.pubKey) == 0 {
		pkx, pky := btcec.S256().ScalarBaseMult(k.key)
		pubKey := btcec.PublicKey{Curve: btcec.S256(), X: pkx, Y: pky}
		k.pubKey = pubKey.SerializeCompressed()
	}

	return k.pubKey
}

// IsPrivate returns whether or not the extended key is a private extended key.
//
// A private extended key can be used to derive both hardened and non-hardened
// child private and public extended keys.  A public extended key can only be
// used to derive non-hardened child public extended keys.
func (k *ExtendedKey) IsPrivate() bool {
	return k.isPrivate
}

// Depth returns the current derivation level with respect to the root.
//
// The root key has depth zero, and the field has a maximum of 255 due to
// how depth is serialized.
func (k *ExtendedKey) Depth() uint8 {
	return k.depth
}

// ParentFingerprint returns a fingerprint of the parent extended key from which
// this one was derived.
func (k *ExtendedKey) ParentFingerprint() uint32 {
	return binary.BigEndian.Uint32(k.parentFP)
}

// Derive returns a derived child extended key at the given index.
//
// IMPORTANT: if you were previously using the Child method, this method is incompatible.
// The Child method had a BIP-32 standard compatibility issue.  You have to check whether
// any hardened derivations in your derivation path are affected by this issue, via the
// IsAffectedByIssue172 method and migrate the wallet if so.  This method does conform
// to the standard.  If you need the old behavior, use DeriveNonStandard.
//
// When this extended key is a private extended key (as determined by the IsPrivate
// function), a private extended key will be derived.  Otherwise, the derived
// extended key will be also be a public extended key.
//
// When the index is greater to or equal than the HardenedKeyStart constant, the
// derived extended key will be a hardened extended key.  It is only possible to
// derive a hardended extended key from a private extended key.  Consequently,
// this function will return ErrDeriveHardFromPublic if a hardened child
// extended key is requested from a public extended key.
//
// A hardened extended key is useful since, as previously mentioned, it requires
// a parent private extended key to derive.  In other words, normal child
// extended public keys can be derived from a parent public extended key (no
// knowledge of the parent private key) whereas hardened extended keys may not
// be.
//
// NOTE: There is an extremely small chance (< 1 in 2^127) the specific child
// index does not derive to a usable child.  The ErrInvalidChild error will be
// returned if this should occur, and the caller is expected to ignore the
// invalid child and simply increment to the next index.
func (k *ExtendedKey) Derive(i uint32) (*ExtendedKey, er.R) {
	// Prevent derivation of children beyond the max allowed depth.
	if k.depth == maxUint8 {
		return nil, ErrDeriveBeyondMaxDepth.Default()
	}

	// There are four scenarios that could happen here:
	// 1) Private extended key -> Hardened child private extended key
	// 2) Private extended key -> Non-hardened child private extended key
	// 3) Public extended key -> Non-hardened child public extended key
	// 4) Public extended key -> Hardened child public extended key (INVALID!)

	// Case #4 is invalid, so error out early.
	// A hardened child extended key may not be created from a public
	// extended key.
	isChildHardened := i >= HardenedKeyStart
	if !k.isPrivate && isChildHardened {
		return nil, ErrDeriveHardFromPublic.Default()
	}

	// The data used to derive the child key depends on whether or not the
	// child is hardened per [BIP32].
	//
	// For hardened children:
	//   0x00 || ser256(parentKey) || ser32(i)
	//
	// For normal children:
	//   serP(parentPubKey) || ser32(i)
	keyLen := 33
	data := make([]byte, keyLen+4)
	if isChildHardened {
		// Case #1.
		// When the child is a hardened child, the key is known to be a
		// private key due to the above early return.  Pad it with a
		// leading zero as required by [BIP32] for deriving the child.
		// Additionally, right align it if it's shorter than 32 bytes.
		offset := 33 - len(k.key)
		copy(data[offset:], k.key)
	} else {
		// Case #2 or #3.
		// This is either a public or private extended key, but in
		// either case, the data which is used to derive the child key
		// starts with the secp256k1 compressed public key bytes.
		copy(data, k.pubKeyBytes())
	}
	binary.BigEndian.PutUint32(data[keyLen:], i)

	// Take the HMAC-SHA512 of the current key's chain code and the derived
	// data:
	//   I = HMAC-SHA512(Key = chainCode, Data = data)
	hmac512 := hmac.New(sha512.New, k.chainCode)
	hmac512.Write(data)
	ilr := hmac512.Sum(nil)

	// Split "I" into two 32-byte sequences Il and Ir where:
	//   Il = intermediate key used to derive the child
	//   Ir = child chain code
	il := ilr[:len(ilr)/2]
	childChainCode := ilr[len(ilr)/2:]

	// Both derived public or private keys rely on treating the left 32-byte
	// sequence calculated above (Il) as a 256-bit integer that must be
	// within the valid range for a secp256k1 private key.  There is a small
	// chance (< 1 in 2^127) this condition will not hold, and in that case,
	// a child extended key can't be created for this index and the caller
	// should simply increment to the next index.
	ilNum := new(big.Int).SetBytes(il)
	if ilNum.Cmp(btcec.S256().N) >= 0 || ilNum.Sign() == 0 {
		return nil, ErrInvalidChild.Default()
	}

	// The algorithm used to derive the child key depends on whether or not
	// a private or public child is being derived.
	//
	// For private children:
	//   childKey = parse256(Il) + parentKey
	//
	// For public children:
	//   childKey = serP(point(parse256(Il)) + parentKey)
	var isPrivate bool
	var childKey []byte
	if k.isPrivate {
		// Case #1 or #2.
		// Add the parent private key to the intermediate private key to
		// derive the final child key.
		//
		// childKey = parse256(Il) + parenKey
		keyNum := new(big.Int).SetBytes(k.key)
		ilNum.Add(ilNum, keyNum)
		ilNum.Mod(ilNum, btcec.S256().N)
		childKey = ilNum.Bytes()
		isPrivate = true
	} else {
		// Case #3.
		// Calculate the corresponding intermediate public key for
		// intermediate private key.
		ilx, ily := btcec.S256().ScalarBaseMult(il)
		if ilx.Sign() == 0 || ily.Sign() == 0 {
			return nil, ErrInvalidChild.Default()
		}

		// Convert the serialized compressed parent public key into X
		// and Y coordinates so it can be added to the intermediate
		// public key.
		pubKey, err := btcec.ParsePubKey(k.key, btcec.S256())
		if err != nil {
			return nil, err
		}

		// Add the intermediate public key to the parent public key to
		// derive the final child key.
		//
		// childKey = serP(point(parse256(Il)) + parentKey)
		childX, childY := btcec.S256().Add(ilx, ily, pubKey.X, pubKey.Y)
		pk := btcec.PublicKey{Curve: btcec.S256(), X: childX, Y: childY}
		childKey = pk.SerializeCompressed()
	}

	// The fingerprint of the parent for the derived child is the first 4
	// bytes of the RIPEMD160(SHA256(parentPubKey)).
	parentFP := btcutil.Hash160(k.pubKeyBytes())[:4]
	return NewExtendedKey(k.version, childKey, childChainCode, parentFP,
		k.depth+1, i, isPrivate), nil
}

// Returns true if this key was affected by the BIP-32 issue in the Child
// method (since renamed to DeriveNonStandard).
func (k *ExtendedKey) IsAffectedByIssue172() bool {
	return len(k.key) < 32
}

// Deprecated: This is a non-standard derivation that is affected by issue #172.
// 1-of-256 hardened derivations will be wrong.  See note in the Derive method
// and IsAffectedByIssue172.
func (k *ExtendedKey) DeriveNonStandard(i uint32) (*ExtendedKey, er.R) {
		// Prevent derivation of children beyond the max allowed depth.
	if k.depth == maxUint8 {
		return nil, ErrDeriveBeyondMaxDepth.Default()
	}

	// There are four scenarios that could happen here:
	// 1) Private extended key -> Hardened child private extended key
	// 2) Private extended key -> Non-hardened child private extended key
	// 3) Public extended key -> Non-hardened child public extended key
	// 4) Public extended key -> Hardened child public extended key (INVALID!)

	// Case #4 is invalid, so error out early.
	// A hardened child extended key may not be created from a public
	// extended key.
	isChildHardened := i >= HardenedKeyStart
	if !k.isPrivate && isChildHardened {
		return nil, ErrDeriveHardFromPublic.Default()
	}

	// The data used to derive the child key depends on whether or not the
	// child is hardened per [BIP32].
	//
	// For hardened children:
	//   0x00 || ser256(parentKey) || ser32(i)
	//
	// For normal children:
	//   serP(parentPubKey) || ser32(i)
	keyLen := 33
	data := make([]byte, keyLen+4)
	if isChildHardened {
		// Case #1.
		// When the child is a hardened child, the key is known to be a
		// private key due to the above early return.  Pad it with a
		// leading zero as required by [BIP32] for deriving the child.
		copy(data[1:], k.key)
	} else {
		// Case #2 or #3.
		// This is either a public or private extended key, but in
		// either case, the data which is used to derive the child key
		// starts with the secp256k1 compressed public key bytes.
		copy(data, k.pubKeyBytes())
	}
	binary.BigEndian.PutUint32(data[keyLen:], i)

	// Take the HMAC-SHA512 of the current key's chain code and the derived
	// data:
	//   I = HMAC-SHA512(Key = chainCode, Data = data)
	hmac512 := hmac.New(sha512.New, k.chainCode)
	hmac512.Write(data)
	ilr := hmac512.Sum(nil)

	// Split "I" into two 32-byte sequences Il and Ir where:
	//   Il = intermediate key used to derive the child
	//   Ir = child chain code
	il := ilr[:len(ilr)/2]
	childChainCode := ilr[len(ilr)/2:]

	// Both derived public or private keys rely on treating the left 32-byte
	// sequence calculated above (Il) as a 256-bit integer that must be
	// within the valid range for a secp256k1 private key.  There is a small
	// chance (< 1 in 2^127) this condition will not hold, and in that case,
	// a child extended key can't be created for this index and the caller
	// should simply increment to the next index.
	ilNum := new(big.Int).SetBytes(il)
	if ilNum.Cmp(btcec.S256().N) >= 0 || ilNum.Sign() == 0 {
		return nil, ErrInvalidChild.Default()
	}

	// The algorithm used to derive the child key depends on whether or not
	// a private or public child is being derived.
	//
	// For private children:
	//   childKey = parse256(Il) + parentKey
	//
	// For public children:
	//   childKey = serP(point(parse256(Il)) + parentKey)
	var isPrivate bool
	var childKey []byte
	if k.isPrivate {
		// Case #1 or #2.
		// Add the parent private key to the intermediate private key to
		// derive the final child key.
		//
		// childKey = parse256(Il) + parenKey
		keyNum := new(big.Int).SetBytes(k.key)
		ilNum.Add(ilNum, keyNum)
		ilNum.Mod(ilNum, btcec.S256().N)
		childKey = ilNum.Bytes()
		isPrivate = true
	} else {
		// Case #3.
		// Calculate the corresponding intermediate public key for
		// intermediate private key.
		ilx, ily := btcec.S256().ScalarBaseMult(il)
		if ilx.Sign() == 0 || ily.Sign() == 0 {
			return nil, ErrInvalidChild.Default()
		}

		// Convert the serialized compressed parent public key into X
		// and Y coordinates so it can be added to the intermediate
		// public key.
		pubKey, err := btcec.ParsePubKey(k.key, btcec.S256())
		if err != nil {
			return nil, err
		}

		// Add the intermediate public key to the parent public key to
		// derive the final child key.
		//
		// childKey = serP(point(parse256(Il)) + parentKey)
		childX, childY := btcec.S256().Add(ilx, ily, pubKey.X, pubKey.Y)
		pk := btcec.PublicKey{Curve: btcec.S256(), X: childX, Y: childY}
		childKey = pk.SerializeCompressed()
	}

	// The fingerprint of the parent for the derived child is the first 4
	// bytes of the RIPEMD160(SHA256(parentPubKey)).
	parentFP := btcutil.Hash160(k.pubKeyBytes())[:4]
	return NewExtendedKey(k.version, childKey, childChainCode, parentFP,
		k.depth+1, i, isPrivate), nil
}

// Neuter returns a new extended public key from this extended private key.  The
// same extended key will be returned unaltered if it is already an extended
// public key.
//
// As the name implies, an extended public key does not have access to the
// private key, so it is not capable of signing transactions or deriving
// child extended private keys.  However, it is capable of deriving further
// child extended public keys.
func (k *ExtendedKey) Neuter() (*ExtendedKey, er.R) {
	// Already an extended public key.
	if !k.isPrivate {
		return k, nil
	}

	// Get the associated public extended key version bytes.
	version, err := chaincfg.HDPrivateKeyToPublicKeyID(k.version)
	if err != nil {
		return nil, err
	}

	// Convert it to an extended public key.  The key for the new extended
	// key will simply be the pubkey of the current extended private key.
	//
	// This is the function N((k,c)) -> (K, c) from [BIP32].
	return NewExtendedKey(version, k.pubKeyBytes(), k.chainCode, k.parentFP,
		k.depth, k.childNum, false), nil
}

// ECPubKey converts the extended key to a btcec public key and returns it.
func (k *ExtendedKey) ECPubKey() (*btcec.PublicKey, er.R) {
	return btcec.ParsePubKey(k.pubKeyBytes(), btcec.S256())
}

// ECPrivKey converts the extended key to a btcec private key and returns it.
// As you might imagine this is only possible if the extended key is a private
// extended key (as determined by the IsPrivate function).  The ErrNotPrivExtKey
// error will be returned if this function is called on a public extended key.
func (k *ExtendedKey) ECPrivKey() (*btcec.PrivateKey, er.R) {
	if !k.isPrivate {
		return nil, ErrNotPrivExtKey.Default()
	}

	privKey, _ := btcec.PrivKeyFromBytes(btcec.S256(), k.key)
	return privKey, nil
}

func (k *ExtendedKey) GetSecret(name []byte) ([]byte, er.R) {
	if !k.isPrivate {
		return nil, ErrNotPrivExtKey.Default()
	}
	if len(k.key) == 0 {
		return nil, ErrNotPrivExtKey.New("Private key has been zeroed", nil)
	}

	sha := sha256.New()
	sha.Write([]byte("GET_SECRET_1"))
	var l [8]byte
	binary.LittleEndian.PutUint64(l[:], uint64(len(name)))
	sha.Write(l[:])
	sha.Write(name)
	sha.Write(k.key)
	return sha.Sum(nil), nil
}

// Address converts the extended key to a standard bitcoin pay-to-pubkey-hash
// address for the passed network.
func (k *ExtendedKey) Address(net *chaincfg.Params) (*btcutil.AddressPubKeyHash, er.R) {
	pkHash := btcutil.Hash160(k.pubKeyBytes())
	return btcutil.NewAddressPubKeyHash(pkHash, net)
}

// paddedAppend appends the src byte slice to dst, returning the new slice.
// If the length of the source is smaller than the passed size, leading zero
// bytes are appended to the dst slice before appending src.
func paddedAppend(size uint, dst, src []byte) []byte {
	for i := 0; i < int(size)-len(src); i++ {
		dst = append(dst, 0)
	}
	return append(dst, src...)
}

// String returns the extended key as a human-readable base58-encoded string.
func (k *ExtendedKey) String() string {
	if len(k.key) == 0 {
		return "zeroed extended key"
	}

	var childNumBytes [4]byte
	binary.BigEndian.PutUint32(childNumBytes[:], k.childNum)

	// The serialized format is:
	//   version (4) || depth (1) || parent fingerprint (4)) ||
	//   child num (4) || chain code (32) || key data (33) || checksum (4)
	serializedBytes := make([]byte, 0, serializedKeyLen+4)
	serializedBytes = append(serializedBytes, k.version...)
	serializedBytes = append(serializedBytes, k.depth)
	serializedBytes = append(serializedBytes, k.parentFP...)
	serializedBytes = append(serializedBytes, childNumBytes[:]...)
	serializedBytes = append(serializedBytes, k.chainCode...)
	if k.isPrivate {
		serializedBytes = append(serializedBytes, 0x00)
		serializedBytes = paddedAppend(32, serializedBytes, k.key)
	} else {
		serializedBytes = append(serializedBytes, k.pubKeyBytes()...)
	}

	checkSum := chainhash.DoubleHashB(serializedBytes)[:4]
	serializedBytes = append(serializedBytes, checkSum...)
	return base58.Encode(serializedBytes)
}

// IsForNet returns whether or not the extended key is associated with the
// passed bitcoin network.
func (k *ExtendedKey) IsForNet(net *chaincfg.Params) bool {
	return bytes.Equal(k.version, net.HDPrivateKeyID[:]) ||
		bytes.Equal(k.version, net.HDPublicKeyID[:])
}

// SetNet associates the extended key, and any child keys yet to be derived from
// it, with the passed network.
func (k *ExtendedKey) SetNet(net *chaincfg.Params) {
	if k.isPrivate {
		k.version = net.HDPrivateKeyID[:]
	} else {
		k.version = net.HDPublicKeyID[:]
	}
}

// zero sets all bytes in the passed slice to zero.  This is used to
// explicitly clear private key material from memory.
func zero(b []byte) {
	lenb := len(b)
	for i := 0; i < lenb; i++ {
		b[i] = 0
	}
}

// Zero manually clears all fields and bytes in the extended key.  This can be
// used to explicitly clear key material from memory for enhanced security
// against memory scraping.  This function only clears this particular key and
// not any children that have already been derived.
func (k *ExtendedKey) Zero() {
	zero(k.key)
	zero(k.pubKey)
	zero(k.chainCode)
	zero(k.parentFP)
	k.version = nil
	k.key = nil
	k.depth = 0
	k.childNum = 0
	k.isPrivate = false
}

// NewMaster creates a new master node for use in creating a hierarchical
// deterministic key chain.  The seed must be between 128 and 512 bits and
// should be generated by a cryptographically secure random generation source.
//
// NOTE: There is an extremely small chance (< 1 in 2^127) the provided seed
// will derive to an unusable secret key.  The ErrUnusable error will be
// returned if this should occur, so the caller must check for it and generate a
// new seed accordingly.
func NewMaster(seed []byte, net *chaincfg.Params) (*ExtendedKey, er.R) {
	// Per [BIP32], the seed must be in range [MinSeedBytes, MaxSeedBytes].
	if len(seed) < MinSeedBytes || len(seed) > MaxSeedBytes {
		return nil, ErrInvalidSeedLen.Default()
	}

	// First take the HMAC-SHA512 of the master key and the seed data:
	//   I = HMAC-SHA512(Key = "Bitcoin seed", Data = S)
	hmac512 := hmac.New(sha512.New, masterKey)
	hmac512.Write(seed)
	lr := hmac512.Sum(nil)

	// Split "I" into two 32-byte sequences Il and Ir where:
	//   Il = master secret key
	//   Ir = master chain code
	secretKey := lr[:len(lr)/2]
	chainCode := lr[len(lr)/2:]

	// Ensure the key in usable.
	secretKeyNum := new(big.Int).SetBytes(secretKey)
	if secretKeyNum.Cmp(btcec.S256().N) >= 0 || secretKeyNum.Sign() == 0 {
		return nil, ErrUnusableSeed.Default()
	}

	parentFP := []byte{0x00, 0x00, 0x00, 0x00}
	return NewExtendedKey(net.HDPrivateKeyID[:], secretKey, chainCode,
		parentFP, 0, 0, true), nil
}

// NewKeyFromString returns a new extended key instance from a base58-encoded
// extended key.
func NewKeyFromString(key string) (*ExtendedKey, er.R) {
	// The base58-decoded extended key must consist of a serialized payload
	// plus an additional 4 bytes for the checksum.
	decoded := base58.Decode(key)
	if len(decoded) != serializedKeyLen+4 {
		return nil, ErrInvalidKeyLen.Default()
	}

	// The serialized format is:
	//   version (4) || depth (1) || parent fingerprint (4)) ||
	//   child num (4) || chain code (32) || key data (33) || checksum (4)

	// Split the payload and checksum up and ensure the checksum matches.
	payload := decoded[:len(decoded)-4]
	checkSum := decoded[len(decoded)-4:]
	expectedCheckSum := chainhash.DoubleHashB(payload)[:4]
	if !bytes.Equal(checkSum, expectedCheckSum) {
		return nil, ErrBadChecksum.Default()
	}

	// Deserialize each of the payload fields.
	version := payload[:4]
	depth := payload[4:5][0]
	parentFP := payload[5:9]
	childNum := binary.BigEndian.Uint32(payload[9:13])
	chainCode := payload[13:45]
	keyData := payload[45:78]

	// The key data is a private key if it starts with 0x00.  Serialized
	// compressed pubkeys either start with 0x02 or 0x03.
	isPrivate := keyData[0] == 0x00
	if isPrivate {
		// Ensure the private key is valid.  It must be within the range
		// of the order of the secp256k1 curve and not be 0.
		keyData = keyData[1:]
		keyNum := new(big.Int).SetBytes(keyData)
		if keyNum.Cmp(btcec.S256().N) >= 0 || keyNum.Sign() == 0 {
			return nil, ErrUnusableSeed.Default()
		}
	} else {
		// Ensure the public key parses correctly and is actually on the
		// secp256k1 curve.
		_, err := btcec.ParsePubKey(keyData, btcec.S256())
		if err != nil {
			return nil, err
		}
	}

	return NewExtendedKey(version, keyData, chainCode, parentFP, depth,
		childNum, isPrivate), nil
}

// GenerateSeed returns a cryptographically secure random seed that can be used
// as the input for the NewMaster function to generate a new master node.
//
// The length is in bytes and it must be between 16 and 64 (128 to 512 bits).
// The recommended length is 32 (256 bits) as defined by the RecommendedSeedLen
// constant.
func GenerateSeed(length uint8) ([]byte, er.R) {
	// Per [BIP32], the seed must be in range [MinSeedBytes, MaxSeedBytes].
	if length < MinSeedBytes || length > MaxSeedBytes {
		return nil, ErrInvalidSeedLen.Default()
	}

	buf := make([]byte, length)
	_, err := rand.Read(buf)
	if err != nil {
		return nil, er.E(err)
	}

	return buf, nil
}