rust-bitcoin-unsafe-fast/src/util/bip32.rs

// Rust Bitcoin Library
// Written in 2014 by
//     Andrew Poelstra <apoelstra@wpsoftware.net>
// To the extent possible under law, the author(s) have dedicated all
// copyright and related and neighboring rights to this software to
// the public domain worldwide. This software is distributed without
// any warranty.
//
// You should have received a copy of the CC0 Public Domain Dedication
// along with this software.
// If not, see <http://creativecommons.org/publicdomain/zero/1.0/>.
//

//! # BIP32 Implementation
//!
//! Implementation of BIP32 hierarchical deterministic wallets, as defined
//! at https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki

use std::default::Default;
use std::io::Cursor;
use std::{error, fmt};
use std::str::FromStr;
use std::string::ToString;
use serde::{Serialize, Deserialize, Serializer, Deserializer};

use byteorder::{BigEndian, ByteOrder, ReadBytesExt};
use crypto::digest::Digest;
use crypto::hmac::Hmac;
use crypto::mac::Mac;
use crypto::ripemd160::Ripemd160;
use secp256k1::key::{PublicKey, SecretKey};
use secp256k1::{self, Secp256k1};

use network::constants::Network;
use util::base58;

#[cfg(feature="fuzztarget")]      use util::sha2::{Sha256, Sha512};
#[cfg(not(feature="fuzztarget"))] use crypto::sha2::{Sha256, Sha512};

/// A chain code
pub struct ChainCode([u8; 32]);
impl_array_newtype!(ChainCode, u8, 32);
impl_array_newtype_show!(ChainCode);
impl_array_newtype_encodable!(ChainCode, u8, 32);

/// A fingerprint
pub struct Fingerprint([u8; 4]);
impl_array_newtype!(Fingerprint, u8, 4);
impl_array_newtype_show!(Fingerprint);
impl_array_newtype_encodable!(Fingerprint, u8, 4);

impl Default for Fingerprint {
    fn default() -> Fingerprint { Fingerprint([0, 0, 0, 0]) }
}

/// Extended private key
#[derive(Copy, Clone, PartialEq, Eq, Debug)]
pub struct ExtendedPrivKey {
    /// The network this key is to be used on
    pub network: Network,
    /// How many derivations this key is from the master (which is 0)
    pub depth: u8,
    /// Fingerprint of the parent key (0 for master)
    pub parent_fingerprint: Fingerprint,
    /// Child number of the key used to derive from parent (0 for master)
    pub child_number: ChildNumber,
    /// Secret key
    pub secret_key: SecretKey,
    /// Chain code
    pub chain_code: ChainCode
}

/// Extended public key
#[derive(Copy, Clone, PartialEq, Eq, Debug)]
pub struct ExtendedPubKey {
    /// The network this key is to be used on
    pub network: Network,
    /// How many derivations this key is from the master (which is 0)
    pub depth: u8,
    /// Fingerprint of the parent key
    pub parent_fingerprint: Fingerprint,
    /// Child number of the key used to derive from parent (0 for master)
    pub child_number: ChildNumber,
    /// Public key
    pub public_key: PublicKey,
    /// Chain code
    pub chain_code: ChainCode
}

/// A child number for a derived key
#[derive(Copy, Clone, PartialEq, Eq, Debug)]
pub enum ChildNumber {
    /// Hardened key index, within [0, 2^31 - 1]
    Hardened(u32),
    /// Non-hardened key, within [0, 2^31 - 1]
    Normal(u32),
}

impl fmt::Display for ChildNumber {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        match *self {
            ChildNumber::Hardened(n) => write!(f, "{}h", n),
            ChildNumber::Normal(n) => write!(f, "{}", n)
        }
    }
}

impl Serialize for ChildNumber {
    fn serialize<S>(&self, s: &mut S) -> Result<(), S::Error>
            where S: Serializer {
        match *self {
            ChildNumber::Hardened(n) => (n + (1 << 31)).serialize(s),
            ChildNumber::Normal(n)     => n.serialize(s)
        }
    }
}

impl Deserialize for ChildNumber {
    fn deserialize<D>(d: &mut D) -> Result<ChildNumber, D::Error>
            where D: Deserializer {
        let n: u32 = try!(Deserialize::deserialize(d));
        if n < (1 << 31) {
            Ok(ChildNumber::Normal(n))
        } else {
            Ok(ChildNumber::Hardened(n - (1 << 31)))
        }
    }
}

/// A BIP32 error
#[derive(Clone, PartialEq, Eq, Debug)]
pub enum Error {
    /// A pk->pk derivation was attempted on a hardened key
    CannotDeriveFromHardenedKey,
    /// A secp256k1 error occured
    Ecdsa(secp256k1::Error),
    /// A child number was provided that was out of range
    InvalidChildNumber(ChildNumber),
    /// Error creating a master seed --- for application use
    RngError(String)
}

impl fmt::Display for Error {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        match *self {
            Error::CannotDeriveFromHardenedKey => f.write_str("cannot derive hardened key from public key"),
            Error::Ecdsa(ref e) => fmt::Display::fmt(e, f),
            Error::InvalidChildNumber(ref n) => write!(f, "child number {} is invalid", n),
            Error::RngError(ref s) => write!(f, "rng error {}", s)
        }
    }
}

impl error::Error for Error {
    fn cause(&self) -> Option<&error::Error> {
       if let Error::Ecdsa(ref e) = *self {
           Some(e)
       } else {
           None
       }
    }

    fn description(&self) -> &str {
        match *self {
            Error::CannotDeriveFromHardenedKey => "cannot derive hardened key from public key",
            Error::Ecdsa(ref e) => error::Error::description(e),
            Error::InvalidChildNumber(_) => "child number is invalid",
            Error::RngError(_) => "rng error"
        }
    }
}

impl From<secp256k1::Error> for Error {
    fn from(e: secp256k1::Error) -> Error { Error::Ecdsa(e) }
}

impl ExtendedPrivKey {
    /// Construct a new master key from a seed value
    pub fn new_master(secp: &Secp256k1, network: Network, seed: &[u8]) -> Result<ExtendedPrivKey, Error> {
        let mut result = [0; 64];
        let mut hmac = Hmac::new(Sha512::new(), b"Bitcoin seed");
        hmac.input(seed);
        hmac.raw_result(&mut result);

        Ok(ExtendedPrivKey {
            network: network,
            depth: 0,
            parent_fingerprint: Default::default(),
            child_number: ChildNumber::Normal(0),
            secret_key: try!(SecretKey::from_slice(secp, &result[..32]).map_err(Error::Ecdsa)),
            chain_code: ChainCode::from(&result[32..])
        })
    }

    /// Creates a privkey from a path
    pub fn from_path(secp: &Secp256k1, master: &ExtendedPrivKey, path: &[ChildNumber])
                     -> Result<ExtendedPrivKey, Error> {
        let mut sk = *master;
        for &num in path.iter() {
            sk = try!(sk.ckd_priv(secp, num));
        }
        Ok(sk)
    }

    /// Private->Private child key derivation
    pub fn ckd_priv(&self, secp: &Secp256k1, i: ChildNumber) -> Result<ExtendedPrivKey, Error> {
        let mut result = [0; 64];
        let mut hmac = Hmac::new(Sha512::new(), &self.chain_code[..]);
        let mut be_n = [0; 4];
        match i {
            ChildNumber::Normal(n) => {
                if n >= (1 << 31) { return Err(Error::InvalidChildNumber(i)) }
                // Non-hardened key: compute public data and use that
                hmac.input(&PublicKey::from_secret_key(secp, &self.secret_key).unwrap().serialize()[..]);
                BigEndian::write_u32(&mut be_n, n);
            }
            ChildNumber::Hardened(n) => {
                if n >= (1 << 31) { return Err(Error::InvalidChildNumber(i)) }
                // Hardened key: use only secret data to prevent public derivation
                hmac.input(&[0u8]);
                hmac.input(&self.secret_key[..]);
                BigEndian::write_u32(&mut be_n, n + (1 << 31));
            }
        }
        hmac.input(&be_n);
        hmac.raw_result(&mut result);
        let mut sk = try!(SecretKey::from_slice(secp, &result[..32]).map_err(Error::Ecdsa));
        try!(sk.add_assign(secp, &self.secret_key).map_err(Error::Ecdsa));

        Ok(ExtendedPrivKey {
            network: self.network,
            depth: self.depth + 1,
            parent_fingerprint: self.fingerprint(secp),
            child_number: i,
            secret_key: sk,
            chain_code: ChainCode::from(&result[32..])
        })
    }

    /// Returns the HASH160 of the chaincode
    pub fn identifier(&self, secp: &Secp256k1) -> [u8; 20] {
        let mut sha2_res = [0; 32];
        let mut ripemd_res = [0; 20];
        // Compute extended public key
        let pk = ExtendedPubKey::from_private(secp, self);
        // Do SHA256 of just the ECDSA pubkey
        let mut sha2 = Sha256::new();
        sha2.input(&pk.public_key.serialize()[..]);
        sha2.result(&mut sha2_res);
        // do RIPEMD160
        let mut ripemd = Ripemd160::new();
        ripemd.input(&sha2_res);
        ripemd.result(&mut ripemd_res);
        // Return
        ripemd_res
    }

    /// Returns the first four bytes of the identifier
    pub fn fingerprint(&self, secp: &Secp256k1) -> Fingerprint {
        Fingerprint::from(&self.identifier(secp)[0..4])
    }
}

impl ExtendedPubKey {
    /// Derives a public key from a private key
    pub fn from_private(secp: &Secp256k1, sk: &ExtendedPrivKey) -> ExtendedPubKey {
        ExtendedPubKey {
            network: sk.network,
            depth: sk.depth,
            parent_fingerprint: sk.parent_fingerprint,
            child_number: sk.child_number,
            public_key: PublicKey::from_secret_key(secp, &sk.secret_key).unwrap(),
            chain_code: sk.chain_code
        }
    }

    /// Compute the scalar tweak added to this key to get a child key
    pub fn ckd_pub_tweak(&self, secp: &Secp256k1, i: ChildNumber) -> Result<(SecretKey, ChainCode), Error> {
        match i {
            ChildNumber::Hardened(n) => {
                if n >= (1 << 31) {
                    Err(Error::InvalidChildNumber(i))
                } else {
                    Err(Error::CannotDeriveFromHardenedKey)
                }
            }
            ChildNumber::Normal(n) => {
                let mut hmac = Hmac::new(Sha512::new(), &self.chain_code[..]);
                hmac.input(&self.public_key.serialize()[..]);
                let mut be_n = [0; 4];
                BigEndian::write_u32(&mut be_n, n);
                hmac.input(&be_n);

                let mut result = [0; 64];
                hmac.raw_result(&mut result);

                let secret_key = try!(SecretKey::from_slice(secp, &result[..32]));
                let chain_code = ChainCode::from(&result[32..]);
                Ok((secret_key, chain_code))
            }
        }
    }

    /// Public->Public child key derivation
    pub fn ckd_pub(&self, secp: &Secp256k1, i: ChildNumber) -> Result<ExtendedPubKey, Error> {
        let (sk, chain_code) = try!(self.ckd_pub_tweak(secp, i));
        let mut pk = self.public_key.clone();
        try!(pk.add_exp_assign(secp, &sk).map_err(Error::Ecdsa));

        Ok(ExtendedPubKey {
            network: self.network,
            depth: self.depth + 1,
            parent_fingerprint: self.fingerprint(),
            child_number: i,
            public_key: pk,
            chain_code: chain_code
        })
    }

    /// Returns the HASH160 of the chaincode
    pub fn identifier(&self) -> [u8; 20] {
        let mut sha2_res = [0; 32];
        let mut ripemd_res = [0; 20];
        // Do SHA256 of just the ECDSA pubkey
        let mut sha2 = Sha256::new();
        sha2.input(&self.public_key.serialize()[..]);
        sha2.result(&mut sha2_res);
        // do RIPEMD160
        let mut ripemd = Ripemd160::new();
        ripemd.input(&sha2_res);
        ripemd.result(&mut ripemd_res);
        // Return
        ripemd_res
    }

    /// Returns the first four bytes of the identifier
    pub fn fingerprint(&self) -> Fingerprint {
        Fingerprint::from(&self.identifier()[0..4])
    }
}

impl ToString for ExtendedPrivKey {
    fn to_string(&self) -> String {
        let mut ret = [0; 78];
        ret[0..4].copy_from_slice(&match self.network {
            Network::Bitcoin => [0x04, 0x88, 0xAD, 0xE4],
            Network::Testnet | Network::Regtest => [0x04, 0x35, 0x83, 0x94],
        }[..]);
        ret[4] = self.depth as u8;
        ret[5..9].copy_from_slice(&self.parent_fingerprint[..]);
        match self.child_number {
            ChildNumber::Hardened(n) => {
                BigEndian::write_u32(&mut ret[9..13], n + (1 << 31));
            }
            ChildNumber::Normal(n) => {
                BigEndian::write_u32(&mut ret[9..13], n);
            }
        }
        ret[13..45].copy_from_slice(&self.chain_code[..]);
        ret[45] = 0;
        ret[46..78].copy_from_slice(&self.secret_key[..]);
        base58::check_encode_slice(&ret[..])
    }
}

impl FromStr for ExtendedPrivKey {
    type Err = base58::Error;

    fn from_str(inp: &str) -> Result<ExtendedPrivKey, base58::Error> {
        let s = Secp256k1::with_caps(secp256k1::ContextFlag::None);
        let data = try!(base58::from_check(inp));

        if data.len() != 78 {
            return Err(base58::Error::InvalidLength(data.len()));
        }

        let cn_int = Cursor::new(&data[9..13]).read_u32::<BigEndian>().unwrap();
        let child_number = if cn_int < (1 << 31) { ChildNumber::Normal(cn_int) }
                           else { ChildNumber::Hardened(cn_int - (1 << 31)) };

        Ok(ExtendedPrivKey {
            network: if &data[0..4] == [0x04u8, 0x88, 0xAD, 0xE4] {
                Network::Bitcoin
            } else if &data[0..4] == [0x04u8, 0x35, 0x83, 0x94] {
                Network::Testnet
            } else {
                return Err(base58::Error::InvalidVersion((&data[0..4]).to_vec()));
            },
            depth: data[4],
            parent_fingerprint: Fingerprint::from(&data[5..9]),
            child_number: child_number,
            chain_code: ChainCode::from(&data[13..45]),
            secret_key: try!(SecretKey::from_slice(&s,
                             &data[46..78]).map_err(|e|
                                 base58::Error::Other(e.to_string())))
        })
    }
}

impl ToString for ExtendedPubKey {
    fn to_string(&self) -> String {
        let mut ret = [0; 78];
        ret[0..4].copy_from_slice(&match self.network {
            Network::Bitcoin => [0x04u8, 0x88, 0xB2, 0x1E],
            Network::Testnet | Network::Regtest => [0x04u8, 0x35, 0x87, 0xCF],
        }[..]);
        ret[4] = self.depth as u8;
        ret[5..9].copy_from_slice(&self.parent_fingerprint[..]);
        match self.child_number {
            ChildNumber::Hardened(n) => {
                BigEndian::write_u32(&mut ret[9..13], n + (1 << 31));
            }
            ChildNumber::Normal(n) => {
                BigEndian::write_u32(&mut ret[9..13], n);
            }
        }
        ret[13..45].copy_from_slice(&self.chain_code[..]);
        ret[45..78].copy_from_slice(&self.public_key.serialize()[..]);
        base58::check_encode_slice(&ret[..])
    }
}

impl FromStr for ExtendedPubKey {
    type Err = base58::Error;

    fn from_str(inp: &str) -> Result<ExtendedPubKey, base58::Error> {
        let s = Secp256k1::with_caps(secp256k1::ContextFlag::None);
        let data = try!(base58::from_check(inp));

        if data.len() != 78 {
            return Err(base58::Error::InvalidLength(data.len()));
        }

        let cn_int = Cursor::new(&data[9..13]).read_u32::<BigEndian>().unwrap();
        let child_number = if cn_int < (1 << 31) { ChildNumber::Normal(cn_int) }
                           else { ChildNumber::Hardened(cn_int - (1 << 31)) };

        Ok(ExtendedPubKey {
            network: if &data[0..4] == [0x04u8, 0x88, 0xB2, 0x1E] {
                Network::Bitcoin
            } else if &data[0..4] == [0x04u8, 0x35, 0x87, 0xCF] {
                Network::Testnet
            } else {
                return Err(base58::Error::InvalidVersion((&data[0..4]).to_vec()));
            },
            depth: data[4],
            parent_fingerprint: Fingerprint::from(&data[5..9]),
            child_number: child_number,
            chain_code: ChainCode::from(&data[13..45]),
            public_key: try!(PublicKey::from_slice(&s,
                             &data[45..78]).map_err(|e|
                                 base58::Error::Other(e.to_string())))
        })
    }
}

#[cfg(test)]
mod tests {
    use std::str::FromStr;
    use std::string::ToString;

    use secp256k1::Secp256k1;
    use serialize::hex::FromHex;

    use network::constants::Network::{self, Bitcoin};

    use super::{ChildNumber, ExtendedPrivKey, ExtendedPubKey};
    use super::ChildNumber::{Hardened, Normal};

    fn test_path(secp: &Secp256k1,
                 network: Network,
                 seed: &[u8],
                 path: &[ChildNumber],
                 expected_sk: &str,
                 expected_pk: &str) {

        let mut sk = ExtendedPrivKey::new_master(secp, network, seed).unwrap();
        let mut pk = ExtendedPubKey::from_private(secp, &sk);
        // Derive keys, checking hardened and non-hardened derivation
        for &num in path.iter() {
            sk = sk.ckd_priv(secp, num).unwrap();
            match num {
                Normal(_) => {
                    let pk2 = pk.ckd_pub(secp, num).unwrap();
                    pk = ExtendedPubKey::from_private(secp, &sk);
                    assert_eq!(pk, pk2);
                }
                Hardened(_) => {
                    pk = ExtendedPubKey::from_private(secp, &sk);
                }
            }
        }

        // Check result against expected base58
        assert_eq!(&sk.to_string()[..], expected_sk);
        assert_eq!(&pk.to_string()[..], expected_pk);
        // Check decoded base58 against result
        let decoded_sk = ExtendedPrivKey::from_str(expected_sk);
        let decoded_pk = ExtendedPubKey::from_str(expected_pk);
        assert_eq!(Ok(sk), decoded_sk);
        assert_eq!(Ok(pk), decoded_pk);
    }

    #[test]
    fn test_vector_1() {
        let secp = Secp256k1::new();
        let seed = "000102030405060708090a0b0c0d0e0f".from_hex().unwrap();
        // m
        test_path(&secp, Bitcoin, &seed, &[],
                  "xprv9s21ZrQH143K3QTDL4LXw2F7HEK3wJUD2nW2nRk4stbPy6cq3jPPqjiChkVvvNKmPGJxWUtg6LnF5kejMRNNU3TGtRBeJgk33yuGBxrMPHi",
                  "xpub661MyMwAqRbcFtXgS5sYJABqqG9YLmC4Q1Rdap9gSE8NqtwybGhePY2gZ29ESFjqJoCu1Rupje8YtGqsefD265TMg7usUDFdp6W1EGMcet8");

        // m/0h
        test_path(&secp, Bitcoin, &seed, &[Hardened(0)],
                  "xprv9uHRZZhk6KAJC1avXpDAp4MDc3sQKNxDiPvvkX8Br5ngLNv1TxvUxt4cV1rGL5hj6KCesnDYUhd7oWgT11eZG7XnxHrnYeSvkzY7d2bhkJ7",
                  "xpub68Gmy5EdvgibQVfPdqkBBCHxA5htiqg55crXYuXoQRKfDBFA1WEjWgP6LHhwBZeNK1VTsfTFUHCdrfp1bgwQ9xv5ski8PX9rL2dZXvgGDnw");

        // m/0h/1
        test_path(&secp, Bitcoin, &seed, &[Hardened(0), Normal(1)],
                   "xprv9wTYmMFdV23N2TdNG573QoEsfRrWKQgWeibmLntzniatZvR9BmLnvSxqu53Kw1UmYPxLgboyZQaXwTCg8MSY3H2EU4pWcQDnRnrVA1xe8fs",
                   "xpub6ASuArnXKPbfEwhqN6e3mwBcDTgzisQN1wXN9BJcM47sSikHjJf3UFHKkNAWbWMiGj7Wf5uMash7SyYq527Hqck2AxYysAA7xmALppuCkwQ");

        // m/0h/1/2h
        test_path(&secp, Bitcoin, &seed, &[Hardened(0), Normal(1), Hardened(2)],
                  "xprv9z4pot5VBttmtdRTWfWQmoH1taj2axGVzFqSb8C9xaxKymcFzXBDptWmT7FwuEzG3ryjH4ktypQSAewRiNMjANTtpgP4mLTj34bhnZX7UiM",
                  "xpub6D4BDPcP2GT577Vvch3R8wDkScZWzQzMMUm3PWbmWvVJrZwQY4VUNgqFJPMM3No2dFDFGTsxxpG5uJh7n7epu4trkrX7x7DogT5Uv6fcLW5");

        // m/0h/1/2h/2
        test_path(&secp, Bitcoin, &seed, &[Hardened(0), Normal(1), Hardened(2), Normal(2)],
                  "xprvA2JDeKCSNNZky6uBCviVfJSKyQ1mDYahRjijr5idH2WwLsEd4Hsb2Tyh8RfQMuPh7f7RtyzTtdrbdqqsunu5Mm3wDvUAKRHSC34sJ7in334",
                  "xpub6FHa3pjLCk84BayeJxFW2SP4XRrFd1JYnxeLeU8EqN3vDfZmbqBqaGJAyiLjTAwm6ZLRQUMv1ZACTj37sR62cfN7fe5JnJ7dh8zL4fiyLHV");

        // m/0h/1/2h/2/1000000000
        test_path(&secp, Bitcoin, &seed, &[Hardened(0), Normal(1), Hardened(2), Normal(2), Normal(1000000000)],
                  "xprvA41z7zogVVwxVSgdKUHDy1SKmdb533PjDz7J6N6mV6uS3ze1ai8FHa8kmHScGpWmj4WggLyQjgPie1rFSruoUihUZREPSL39UNdE3BBDu76",
                  "xpub6H1LXWLaKsWFhvm6RVpEL9P4KfRZSW7abD2ttkWP3SSQvnyA8FSVqNTEcYFgJS2UaFcxupHiYkro49S8yGasTvXEYBVPamhGW6cFJodrTHy");
    }

    #[test]
    fn test_vector_2() {
        let secp = Secp256k1::new();
        let seed = "fffcf9f6f3f0edeae7e4e1dedbd8d5d2cfccc9c6c3c0bdbab7b4b1aeaba8a5a29f9c999693908d8a8784817e7b7875726f6c696663605d5a5754514e4b484542".from_hex().unwrap();

        // m
        test_path(&secp, Bitcoin, &seed, &[],
                  "xprv9s21ZrQH143K31xYSDQpPDxsXRTUcvj2iNHm5NUtrGiGG5e2DtALGdso3pGz6ssrdK4PFmM8NSpSBHNqPqm55Qn3LqFtT2emdEXVYsCzC2U",
                  "xpub661MyMwAqRbcFW31YEwpkMuc5THy2PSt5bDMsktWQcFF8syAmRUapSCGu8ED9W6oDMSgv6Zz8idoc4a6mr8BDzTJY47LJhkJ8UB7WEGuduB");

        // m/0
        test_path(&secp, Bitcoin, &seed, &[Normal(0)],
                  "xprv9vHkqa6EV4sPZHYqZznhT2NPtPCjKuDKGY38FBWLvgaDx45zo9WQRUT3dKYnjwih2yJD9mkrocEZXo1ex8G81dwSM1fwqWpWkeS3v86pgKt",
                  "xpub69H7F5d8KSRgmmdJg2KhpAK8SR3DjMwAdkxj3ZuxV27CprR9LgpeyGmXUbC6wb7ERfvrnKZjXoUmmDznezpbZb7ap6r1D3tgFxHmwMkQTPH");

        // m/0/2147483647h
        test_path(&secp, Bitcoin, &seed, &[Normal(0), Hardened(2147483647)],
                  "xprv9wSp6B7kry3Vj9m1zSnLvN3xH8RdsPP1Mh7fAaR7aRLcQMKTR2vidYEeEg2mUCTAwCd6vnxVrcjfy2kRgVsFawNzmjuHc2YmYRmagcEPdU9",
                  "xpub6ASAVgeehLbnwdqV6UKMHVzgqAG8Gr6riv3Fxxpj8ksbH9ebxaEyBLZ85ySDhKiLDBrQSARLq1uNRts8RuJiHjaDMBU4Zn9h8LZNnBC5y4a");

        // m/0/2147483647h/1
        test_path(&secp, Bitcoin, &seed, &[Normal(0), Hardened(2147483647), Normal(1)],
                  "xprv9zFnWC6h2cLgpmSA46vutJzBcfJ8yaJGg8cX1e5StJh45BBciYTRXSd25UEPVuesF9yog62tGAQtHjXajPPdbRCHuWS6T8XA2ECKADdw4Ef",
                  "xpub6DF8uhdarytz3FWdA8TvFSvvAh8dP3283MY7p2V4SeE2wyWmG5mg5EwVvmdMVCQcoNJxGoWaU9DCWh89LojfZ537wTfunKau47EL2dhHKon");

        // m/0/2147483647h/1/2147483646h
        test_path(&secp, Bitcoin, &seed, &[Normal(0), Hardened(2147483647), Normal(1), Hardened(2147483646)],
                  "xprvA1RpRA33e1JQ7ifknakTFpgNXPmW2YvmhqLQYMmrj4xJXXWYpDPS3xz7iAxn8L39njGVyuoseXzU6rcxFLJ8HFsTjSyQbLYnMpCqE2VbFWc",
                  "xpub6ERApfZwUNrhLCkDtcHTcxd75RbzS1ed54G1LkBUHQVHQKqhMkhgbmJbZRkrgZw4koxb5JaHWkY4ALHY2grBGRjaDMzQLcgJvLJuZZvRcEL");

        // m/0/2147483647h/1/2147483646h/2
        test_path(&secp, Bitcoin, &seed, &[Normal(0), Hardened(2147483647), Normal(1), Hardened(2147483646), Normal(2)],
                  "xprvA2nrNbFZABcdryreWet9Ea4LvTJcGsqrMzxHx98MMrotbir7yrKCEXw7nadnHM8Dq38EGfSh6dqA9QWTyefMLEcBYJUuekgW4BYPJcr9E7j",
                  "xpub6FnCn6nSzZAw5Tw7cgR9bi15UV96gLZhjDstkXXxvCLsUXBGXPdSnLFbdpq8p9HmGsApME5hQTZ3emM2rnY5agb9rXpVGyy3bdW6EEgAtqt");
    }

    #[test]
    pub fn encode_decode_childnumber() {
        serde_round_trip!(Normal(0));
        serde_round_trip!(Normal(1));
        serde_round_trip!(Normal((1 << 31) - 1));
        serde_round_trip!(Hardened(0));
        serde_round_trip!(Hardened(1));
        serde_round_trip!(Hardened((1 << 31) - 1));
    }
}