bip-0032-关于HDWallet解读 ​

// Child returns a derived child extended key at the given index.  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) Child(i uint32) (*ExtendedKey, error) {
	// Prevent derivation of children beyond the max allowed depth.
	if k.depth == maxUint8 {
		return nil, ErrDeriveBeyondMaxDepth
	}

	// 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
	}

	// 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.
	//这里的2^127是怎么算出来的呢?
	/*
	N=FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141
	如果il是均匀分布,那么出现大于N的可能性是P{il>N}=(MaxUint256-N)/MaxUint256
	约等于1/(2^127)
	但是为什么要排除这种情况,而不是取模呢
	 */
	ilNum := new(big.Int).SetBytes(il)
	if ilNum.Cmp(btcec.S256().N) >= 0 || ilNum.Sign() == 0 {
		return nil, ErrInvalidChild
	}

	// 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
		}

		// 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()
		/*
		childKey对应的私钥是什么呢?
		K1=k1*G
		K2=k2*G
		K3=K1+K2=k1*G+k2*G=(k1+k2)*G
		因此K3对应的私钥是k1+k2
		所以childKey对应的私钥就是il+(k.key 对应的私钥)
		 */
	}

	// 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
}

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:]

ilr:=sha512(0,ParentPrivateKey,index,ParentChainCode)
childPrivateKey:=ilr[:32]
childChainCode:=ilr[32:]

ilr:=sha512(ParentPubicKey,index,ParentChainCode)
childPrivateKey:=ilr[:32]
childChainCode:=ilr[32:]

ilr:=sha512(ParentPubicKey,index,ParentChainCode)
il:=ilr[:32]
childChainCode:=ilr[32:]
 ilx, ily := btcec.S256().ScalarBaseMult(il)
 childX, childY := btcec.S256().Add(ilx, ily, paretPubKey.X, paretPubKey.Y)
 pk := btcec.PublicKey{Curve: btcec.S256(), X: childX, Y: childY}
childPubKey = pk.SerializeCompressed()