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Bitcoin Cross-Platform C++ Development Toolkit

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How to get a Bitcoin address from a mnemonic?

evoskuil opened this issue · comments

commented

Attempt posted by @alonargel

#include <cstdlib>
#include <string>
#include <bitcoin/system.hpp>

BC_USE_LIBBITCOIN_MAIN
LIBBITCOIN_SYSTEM_WALLET_MNEMONICS_MNEMONIC_HPP

int bc::system::main(int argc, char* argv[])
{
    using namespace bc;
    using namespace bc::system;
    using namespace bc::system::wallet;

    std::string mnemonic_phrase = "bunker churn kangaroo melt bleak chalk vacant alert reason exit forward language";
    libbitcoin::system::wallet::mnemonic mnemonic(mnemonic_phrase);

    libbitcoin::system::wallet::hd_private key = mnemonic.to_key();
    system::cout << mnemonic.to_key() << std::endl;

    return 0;
}
commented

The following example demonstrates:

  • derivation of recovery seed from BIP39 mnemonic phrase
  • derivation of account private key from recovery seed
  • derivation of hd hard/soft keys along arbitrary private path
  • derivation of corresponding hd public keys from hd private keys
  • derivation of corresponding ec private keys from hd private keys
  • derivation of corresponding ec public keys from hd private keys
  • derivation of p2pkh and witness addresses from ec private keys
  • derivation of corresponding hd public keys along public path
  • derivation of corresponding ec public keys from hd public keys
  • derivation of p2pkh and witness addresses from ec public keys
  • prefix, chain, version, and compression context for address construction
#include <cstdlib>
#include <bitcoin/system.hpp>

BC_USE_LIBBITCOIN_MAIN

int bc::system::main(int, char*[])
{
    using namespace bc;
    using namespace bc::system;
    using namespace bc::system::wallet;

    set_utf8_stdio();

    // Recovery seed derivation.
    const auto mnemonic_phrase = "bunker churn kangaroo melt bleak chalk vacant alert reason exit forward language";
    const mnemonic recovery_seed(mnemonic_phrase);
    if (!recovery_seed)
    {
        system::cerr << "Invalid mnemonic phrase." << std::endl;
        return EXIT_FAILURE;
    }

    const auto compressed = true;
    const auto context = ctx::btc::main::p2pkh;

    // Account private key derivation.
    const auto passphrase = "";
    const auto account_private_key = recovery_seed.to_key(passphrase, context);
    if (!account_private_key)
    {
        system::cerr << "Unexpected error." << std::endl;
        return EXIT_FAILURE;
    }

    // private
    // ------------------------------------------------------------------------

    // Some hd private key derivations.
    const auto& m = account_private_key;
    const auto m0h = m.derive_private(hd_first_hardened_key);
    const auto m0h1 = m0h.derive_private(1);
    const auto m0h12h = m0h1.derive_private(2 + hd_first_hardened_key);
    const auto m0h12h2 = m0h12h.derive_private(2);
    const auto m0h12h2x = m0h12h2.derive_private(1000000000);

    system::cout << m << std::endl;
    system::cout << m0h << std::endl;
    system::cout << m0h1 << std::endl;
    system::cout << m0h12h << std::endl;
    system::cout << m0h12h2 << std::endl;
    system::cout << m0h12h2x << std::endl;
    system::cout << std::endl;

    // Corresponding hd public key derivations.
    const auto hd_p = m.to_public();
    const auto hd0h_p = m0h.to_public();
    const auto hd0h1_p = m0h1.to_public();
    const auto hd0h12h_p = m0h12h.to_public();
    const auto hd0h12h2_p = m0h12h2.to_public();
    const auto hd0h12h2x_p = m0h12h2x.to_public();

    system::cout << hd_p << std::endl;
    system::cout << hd0h_p << std::endl;
    system::cout << hd0h1_p << std::endl;
    system::cout << hd0h12h_p << std::endl;
    system::cout << hd0h12h2_p  << std::endl;
    system::cout << hd0h12h2x_p << std::endl;
    system::cout << std::endl;

    // Corresponding ec private key derivations.
    const auto ec = m.secret();
    const auto ec0h = m0h.secret();
    const auto ec0h1 = m0h1.secret();
    const auto ec0h12h = m0h12h.secret();
    const auto ec0h12h2 = m0h12h2.secret();
    const auto ec0h12h2x = m0h12h2x.secret();

    system::cout << encode_base16(ec) << std::endl;
    system::cout << encode_base16(ec0h) << std::endl;
    system::cout << encode_base16(ec0h1) << std::endl;
    system::cout << encode_base16(ec0h12h) << std::endl;
    system::cout << encode_base16(ec0h12h2) << std::endl;
    system::cout << encode_base16(ec0h12h2x) << std::endl;
    system::cout << std::endl;

    // Corresponding ec public keys from private.
    const auto ec_p = m.point();
    const auto ec0h_p = m0h.point();
    const auto ec0h1_p = m0h1.point();
    const auto ec0h12h_p = m0h12h.point();
    const auto ec0h12h2_p = m0h12h2.point();
    const auto ec0h12h2x_p = m0h12h2x.point();

    system::cout << encode_base16(ec_p) << std::endl;
    system::cout << encode_base16(ec0h_p) << std::endl;
    system::cout << encode_base16(ec0h1_p) << std::endl;
    system::cout << encode_base16(ec0h12h_p) << std::endl;
    system::cout << encode_base16(ec0h12h2_p) << std::endl;
    system::cout << encode_base16(ec0h12h2x_p) << std::endl;
    system::cout << std::endl;

    // Corresponding witness address derivations from ec private keys.
    // ec_private{} prevents ec_secret (vector) from falling into hash_digest
    // (vector) constructor, as these are byte vectors of the same length.
    const auto witness = witness_address(ec_private{ ec }, context.witness_prefix);
    const auto witness0h = witness_address(ec_private{ ec0h }, context.witness_prefix);
    const auto witness0h1 = witness_address(ec_private{ ec0h1 }, context.witness_prefix);
    const auto witness0h12h = witness_address(ec_private{ ec0h12h }, context.witness_prefix);
    const auto witness0h12h2 = witness_address(ec_private{ ec0h12h2 }, context.witness_prefix);
    const auto witness0h12h2x = witness_address(ec_private{ ec0h12h2x }, context.witness_prefix);

    system::cout << witness << std::endl;
    system::cout << witness0h << std::endl;
    system::cout << witness0h1 << std::endl;
    system::cout << witness0h12h << std::endl;
    system::cout << witness0h12h2 << std::endl;
    system::cout << witness0h12h2x << std::endl;
    system::cout << std::endl;

    // Corresponding payment address derivations from ec private keys.
    // ec_private allows for passage of context (prevents context loss in some situations).
    const auto address = payment_address(ec_private{ ec, context.versions(), compressed });
    const auto address0h = payment_address(ec_private{ ec0h, context.versions(), compressed });
    const auto address0h1 = payment_address(ec_private{ ec0h1, context.versions(), compressed });
    const auto address0h12h = payment_address(ec_private{ ec0h12h, context.versions(), compressed });
    const auto address0h12h2 = payment_address(ec_private{ ec0h12h2, context.versions(), compressed });
    const auto address0h12h2x = payment_address(ec_private{ ec0h12h2x, context.versions(), compressed });

    system::cout << address << std::endl;
    system::cout << address0h << std::endl;
    system::cout << address0h1 << std::endl;
    system::cout << address0h12h << std::endl;
    system::cout << address0h12h2 << std::endl;
    system::cout << address0h12h2x << std::endl;
    system::cout << std::endl;

    // public
    // ------------------------------------------------------------------------

    // Corresponding hd public key derivations.
    const auto m_pub = m.to_public();
    const auto m0h_pub = m.derive_public(hd_first_hardened_key);
    const auto m0h1_pub = m0h.derive_public(1);
    const auto m0h12h_pub = m0h1.derive_public(2 + hd_first_hardened_key);
    const auto m0h12h2_pub = m0h12h.derive_public(2);
    const auto m0h12h2x_pub = m0h12h2.derive_public(1000000000);

    system::cout << m_pub << std::endl;
    system::cout << m0h_pub << std::endl;
    system::cout << m0h1_pub << std::endl;
    system::cout << m0h12h_pub << std::endl;
    system::cout << m0h12h2_pub << std::endl;
    system::cout << m0h12h2x_pub << std::endl;
    system::cout << std::endl;

    // Corresponding ec public key derivations.
    const auto ec_pub = m_pub.point();
    const auto ec0h_pub = m0h_pub.point();
    const auto ec0h1_pub = m0h1_pub.point();
    const auto ec0h12h_pub = m0h12h_pub.point();
    const auto ec0h12h2_pub = m0h12h2_pub.point();
    const auto ec0h12h2x_pub = m0h12h2x_pub.point();

    system::cout << encode_base16(ec_pub) << std::endl;
    system::cout << encode_base16(ec0h_pub) << std::endl;
    system::cout << encode_base16(ec0h1_pub) << std::endl;
    system::cout << encode_base16(ec0h12h_pub) << std::endl;
    system::cout << encode_base16(ec0h12h2_pub) << std::endl;
    system::cout << encode_base16(ec0h12h2x_pub) << std::endl;
    system::cout << std::endl;

    // Corresponding witness address derivations from ec public keys.
    // ec_public{} unnecessary, as ec_compressed is unambiguous 33 byte vector.
    // ec_public does not provide for passage of context (can always be passed locally).
    const auto witness_pub = witness_address(ec_public{ ec_pub, compressed }, context.witness_prefix);
    const auto witness0h_pub = witness_address(ec_public{ ec0h_pub, compressed }, context.witness_prefix);
    const auto witness0h1_pub = witness_address(ec_public{ ec0h1_pub, compressed }, context.witness_prefix);
    const auto witness0h12h_pub = witness_address(ec_public{ ec0h12h_pub, compressed }, context.witness_prefix);
    const auto witness0h12h2_pub = witness_address(ec_public{ ec0h12h2_pub, compressed }, context.witness_prefix);
    const auto witness0h12h2x_pub = witness_address(ec_public{ ec0h12h2x_pub, compressed }, context.witness_prefix);

    system::cout << witness_pub << std::endl;
    system::cout << witness0h_pub << std::endl;
    system::cout << witness0h1_pub << std::endl;
    system::cout << witness0h12h_pub << std::endl;
    system::cout << witness0h12h2_pub << std::endl;
    system::cout << witness0h12h2x_pub << std::endl;
    system::cout << std::endl;

    // Corresponding payment address derivations from ec public keys.
    const auto address_pub = payment_address(ec_pub, context.address_version);
    const auto address0h_pub = payment_address(ec0h_pub, context.address_version);
    const auto address0h1_pub = payment_address(ec0h1_pub, context.address_version);
    const auto address0h12h_pub = payment_address(ec0h12h_pub, context.address_version);
    const auto address0h12h2_pub = payment_address(ec0h12h2_pub, context.address_version);
    const auto address0h12h2x_pub = payment_address(ec0h12h2x_pub, context.address_version);

    system::cout << address_pub << std::endl;
    system::cout << address0h_pub << std::endl;
    system::cout << address0h1_pub << std::endl;
    system::cout << address0h12h_pub << std::endl;
    system::cout << address0h12h2_pub << std::endl;
    system::cout << address0h12h2x_pub << std::endl;
    system::cout << std::endl;

    return EXIT_SUCCESS;
}
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commented

There are examples of these in the corresponding unit test cases. Hope this helps.

commented

There are examples of these in the corresponding unit test cases. Hope this helps.

Thank you very much for your example, everything compiled perfectly, but there is one thing, addresses do not match the mnemonic phrase in the example, maybe I don’t understand something? I checked with https://iancoleman.io/bip39/
BIP44
bunker churn kangaroo melt bleak chalk vacant alert reason exit forward language

m/44'/0'/0'/0/0 16FdACJs8hU8yZYLPP85KX5WH5wqHmsh4r 02ab0375a86623124a63483f439fe46026ff2ef0165687be7d06618450c37b54f4 L1aceRm4wqdEfFW3dCtLJhFEjRu7cmBHXRLQ4rkbkq144aw1cYky

m/44'/0'/0'/0/1 1P8AaRKzWSTVaTGZA46Vh9J7vzp6r4q4eT 0221ce5e67d16ffc619bfbfa8f0f392c3c6e09ce7358ed1cb63b6de695336a5b36 L5TBqmGv6P4ecBCH6P9ZaC888FLPwzGeUqQxRey1pKCND5GpMTLj

m/44'/0'/0'/0/2 1Mc6Nig43ppeVn1p7PeVkY2gaDNx8CovuF 02499e0fcc1d8382ed2ddbe71211feddcfd18f5d518a6215581e179fe34659e246 L1BXqL6HDZ7uFdcTLFxTrHJjAPa4aYdnVMa9BmFgwQZhQ2JBtpA3

m/44'/0'/0'/0/3 192vVrJzKcPGXf2oDDecC1G2XFjmBVf5sc 026f8a4814af6e4e8175303c48d2574b6b472d114e1114a1a4832cc65fa2b3c193 L5TtRy6agRVVLxrw98R4B4ALgWwMgyJL8W4kphNk5Kehbr3aC7CW

commented

These are HD derivation paths, the example shows how to navigate these. The path m/44'/0'/0'/0/3 represents a derivation of: 44 hardened, 0 hardened, 0 hardened, 0, 3. There is presently no BIP44 helper to convert the path and master key to a derived key, but it is trivially walked once you have a parsed path.

This might also help, though it's for v3 it's still very close. https://github.com/libbitcoin/libbitcoin-system/wiki/Addresses-and-HD-Wallets

commented

The full path in the sample code above is m/0'/1/2'/2/1000000000 and the output matches that on https://iancoleman.io/bip39/

image

commented

I eliminated some unnecessary copies, added WIF conversions/output, and added your first derivation as the last output of each section. You can see that this matches your intended output.

#include <cstdlib>
#include <bitcoin/system.hpp>

BC_USE_LIBBITCOIN_MAIN

int bc::system::main(int, char*[])
{
    using namespace bc;
    using namespace bc::system;
    using namespace bc::system::wallet;

    set_utf8_stdio();

    // Recovery seed derivation.
    const auto mnemonic_phrase = "bunker churn kangaroo melt bleak chalk vacant alert reason exit forward language";
    const mnemonic recovery_seed(mnemonic_phrase);
    if (!recovery_seed)
    {
        system::cerr << "Invalid mnemonic phrase." << std::endl;
        return EXIT_FAILURE;
    }

    const auto compressed = true;
    const auto context = ctx::btc::main::p2pkh;

    // Account private key derivation.
    const auto passphrase = "";
    const auto account_private_key = recovery_seed.to_key(passphrase, context);
    if (!account_private_key)
    {
        system::cerr << "Unexpected error." << std::endl;
        return EXIT_FAILURE;
    }

    // private
    // ------------------------------------------------------------------------

    // Some hd private key derivations.
    const auto& m = account_private_key;
    const auto m0h = m.derive_private(hd_first_hardened_key);
    const auto m0h1 = m0h.derive_private(1);
    const auto m0h12h = m0h1.derive_private(2 + hd_first_hardened_key);
    const auto m0h12h2 = m0h12h.derive_private(2);
    const auto m0h12h2x = m0h12h2.derive_private(1000000000);
    const auto m44h0h0h00 = m
        .derive_private(44 + hd_first_hardened_key)
        .derive_private(0 + hd_first_hardened_key)
        .derive_private(0 + hd_first_hardened_key)
        .derive_private(0)
        .derive_private(0);

    system::cout << m << std::endl;
    system::cout << m0h << std::endl;
    system::cout << m0h1 << std::endl;
    system::cout << m0h12h << std::endl;
    system::cout << m0h12h2 << std::endl;
    system::cout << m0h12h2x << std::endl;
    system::cout << m44h0h0h00 << std::endl;
    system::cout << std::endl;

    // Corresponding hd public key derivations.
    const auto hd_p = m.to_public();
    const auto hd0h_p = m0h.to_public();
    const auto hd0h1_p = m0h1.to_public();
    const auto hd0h12h_p = m0h12h.to_public();
    const auto hd0h12h2_p = m0h12h2.to_public();
    const auto hd0h12h2x_p = m0h12h2x.to_public();
    const auto m44h0h0h00_p = m44h0h0h00.to_public();

    system::cout << hd_p << std::endl;
    system::cout << hd0h_p << std::endl;
    system::cout << hd0h1_p << std::endl;
    system::cout << hd0h12h_p << std::endl;
    system::cout << hd0h12h2_p  << std::endl;
    system::cout << hd0h12h2x_p << std::endl;
    system::cout << m44h0h0h00_p << std::endl;
    system::cout << std::endl;

    // Corresponding ec private key derivations.
    const auto& ec = m.secret();
    const auto& ec0h = m0h.secret();
    const auto& ec0h1 = m0h1.secret();
    const auto& ec0h12h = m0h12h.secret();
    const auto& ec0h12h2 = m0h12h2.secret();
    const auto& ec0h12h2x = m0h12h2x.secret();
    const auto& ec44h0h0h00 = m44h0h0h00.secret();

    system::cout << encode_base16(ec) << std::endl;
    system::cout << encode_base16(ec0h) << std::endl;
    system::cout << encode_base16(ec0h1) << std::endl;
    system::cout << encode_base16(ec0h12h) << std::endl;
    system::cout << encode_base16(ec0h12h2) << std::endl;
    system::cout << encode_base16(ec0h12h2x) << std::endl;
    system::cout << encode_base16(ec44h0h0h00) << std::endl;
    system::cout << std::endl;

    // Corresponding WIF (ec_private) key conversions.
    const ec_private wif{ ec };
    const ec_private wif0h{ ec0h };
    const ec_private wif0h1{ ec0h1 };
    const ec_private wif0h12h{ ec0h12h };
    const ec_private wif0h12h2{ ec0h12h2 };
    const ec_private wif0h12h2x{ ec0h12h2x };
    const ec_private wif44h0h0h00{ ec44h0h0h00 };

    system::cout << wif << std::endl;
    system::cout << wif0h << std::endl;
    system::cout << wif0h1 << std::endl;
    system::cout << wif0h12h << std::endl;
    system::cout << wif0h12h2 << std::endl;
    system::cout << wif0h12h2x << std::endl;
    system::cout << wif44h0h0h00 << std::endl;
    system::cout << std::endl;

    // Corresponding ec public keys from private.
    const auto& ec_p = m.point();
    const auto& ec0h_p = m0h.point();
    const auto& ec0h1_p = m0h1.point();
    const auto& ec0h12h_p = m0h12h.point();
    const auto& ec0h12h2_p = m0h12h2.point();
    const auto& ec0h12h2x_p = m0h12h2x.point();
    const auto& ec44h0h0h00_p = m44h0h0h00.point();

    system::cout << encode_base16(ec_p) << std::endl;
    system::cout << encode_base16(ec0h_p) << std::endl;
    system::cout << encode_base16(ec0h1_p) << std::endl;
    system::cout << encode_base16(ec0h12h_p) << std::endl;
    system::cout << encode_base16(ec0h12h2_p) << std::endl;
    system::cout << encode_base16(ec0h12h2x_p) << std::endl;
    system::cout << encode_base16(ec44h0h0h00_p) << std::endl;
    system::cout << std::endl;

    // Corresponding witness address derivations from WIF (ec private) keys.
    const witness_address witness{ wif, context.witness_prefix };
    const witness_address witness0h{ wif0h, context.witness_prefix };
    const witness_address witness0h1{ wif0h1, context.witness_prefix };
    const witness_address witness0h12h{ wif0h12h, context.witness_prefix };
    const witness_address witness0h12h2{ wif0h12h2, context.witness_prefix };
    const witness_address witness0h12h2x{ wif0h12h2x, context.witness_prefix };
    const witness_address witness44h0h0h00{ wif44h0h0h00, context.witness_prefix };

    system::cout << witness << std::endl;
    system::cout << witness0h << std::endl;
    system::cout << witness0h1 << std::endl;
    system::cout << witness0h12h << std::endl;
    system::cout << witness0h12h2 << std::endl;
    system::cout << witness0h12h2x << std::endl;
    system::cout << witness44h0h0h00 << std::endl;
    system::cout << std::endl;

    // Corresponding payment address derivations from ec private keys.
    // ec_private allows for passage of context (prevents context loss in some situations).
    const payment_address address{ ec_private{ ec, context.versions(), compressed } };
    const payment_address address0h{ ec_private{ ec0h, context.versions(), compressed } };
    const payment_address address0h1{ ec_private{ ec0h1, context.versions(), compressed } };
    const payment_address address0h12h{ ec_private{ ec0h12h, context.versions(), compressed } };
    const payment_address address0h12h2{ ec_private{ ec0h12h2, context.versions(), compressed } };
    const payment_address address0h12h2x{ ec_private{ ec0h12h2x, context.versions(), compressed } };
    const payment_address address44h0h0h00{ ec_private{ ec44h0h0h00, context.versions(), compressed } };

    system::cout << address << std::endl;
    system::cout << address0h << std::endl;
    system::cout << address0h1 << std::endl;
    system::cout << address0h12h << std::endl;
    system::cout << address0h12h2 << std::endl;
    system::cout << address0h12h2x << std::endl;
    system::cout << address44h0h0h00 << std::endl;
    system::cout << std::endl;

    // public
    // ------------------------------------------------------------------------

    // Corresponding hd public key derivations .
    const auto m_pub = m.to_public();
    const auto m0h_pub = m.derive_public(hd_first_hardened_key);
    const auto m0h1_pub = m0h.derive_public(1);
    const auto m0h12h_pub = m0h1.derive_public(2 + hd_first_hardened_key);
    const auto m0h12h2_pub = m0h12h.derive_public(2);
    const auto m0h12h2x_pub = m0h12h2.derive_public(1000000000);
    const auto m44h0h0h00_pub = m
        .derive_private(44 + hd_first_hardened_key) // hardened requires private derivation
        .derive_private(0 + hd_first_hardened_key)  // hardened requires private derivation
        .derive_public(0 + hd_first_hardened_key)
        .derive_public(0)
        .derive_public(0);

    system::cout << m_pub << std::endl;
    system::cout << m0h_pub << std::endl;
    system::cout << m0h1_pub << std::endl;
    system::cout << m0h12h_pub << std::endl;
    system::cout << m0h12h2_pub << std::endl;
    system::cout << m0h12h2x_pub << std::endl;
    system::cout << m44h0h0h00_pub << std::endl;
    system::cout << std::endl;

    // Corresponding ec public key derivations.
    const auto& ec_pub = m_pub.point();
    const auto& ec0h_pub = m0h_pub.point();
    const auto& ec0h1_pub = m0h1_pub.point();
    const auto& ec0h12h_pub = m0h12h_pub.point();
    const auto& ec0h12h2_pub = m0h12h2_pub.point();
    const auto& ec0h12h2x_pub = m0h12h2x_pub.point();
    const auto& ec44h0h0h00_pub = m44h0h0h00_pub.point();

    system::cout << encode_base16(ec_pub) << std::endl;
    system::cout << encode_base16(ec0h_pub) << std::endl;
    system::cout << encode_base16(ec0h1_pub) << std::endl;
    system::cout << encode_base16(ec0h12h_pub) << std::endl;
    system::cout << encode_base16(ec0h12h2_pub) << std::endl;
    system::cout << encode_base16(ec0h12h2x_pub) << std::endl;
    system::cout << encode_base16(ec44h0h0h00_pub) << std::endl;
    system::cout << std::endl;

    // Corresponding witness address derivations from ec public keys.
    // ec_public{} unnecessary, as ec_compressed is unambiguous 33 byte vector.
    // ec_public does not provide for passage of context (can always be passed locally).
    const witness_address witness_pub{ ec_public{ ec_pub, compressed }, context.witness_prefix };
    const witness_address witness0h_pub{ ec_public{ ec0h_pub, compressed }, context.witness_prefix };
    const witness_address witness0h1_pub{ ec_public{ ec0h1_pub, compressed }, context.witness_prefix };
    const witness_address witness0h12h_pub{ ec_public{ ec0h12h_pub, compressed }, context.witness_prefix };
    const witness_address witness0h12h2_pub{ ec_public{ ec0h12h2_pub, compressed }, context.witness_prefix };
    const witness_address witness0h12h2x_pub{ ec_public{ ec0h12h2x_pub, compressed }, context.witness_prefix };
    const witness_address witness44h0h0h00_pub{ ec_public{ ec44h0h0h00_pub, compressed }, context.witness_prefix };

    system::cout << witness_pub << std::endl;
    system::cout << witness0h_pub << std::endl;
    system::cout << witness0h1_pub << std::endl;
    system::cout << witness0h12h_pub << std::endl;
    system::cout << witness0h12h2_pub << std::endl;
    system::cout << witness0h12h2x_pub << std::endl;
    system::cout << witness44h0h0h00_pub << std::endl;
    system::cout << std::endl;

    // Corresponding payment address derivations from ec public keys.
    const payment_address address_pub{ ec_pub, context.address_version };
    const payment_address address0h_pub{ ec0h_pub, context.address_version };
    const payment_address address0h1_pub{ ec0h1_pub, context.address_version };
    const payment_address address0h12h_pub{ ec0h12h_pub, context.address_version };
    const payment_address address0h12h2_pub{ ec0h12h2_pub, context.address_version };
    const payment_address address0h12h2x_pub{ ec0h12h2x_pub, context.address_version };
    const payment_address address44h0h0h00_pub{ ec44h0h0h00_pub, context.address_version };

    system::cout << address_pub << std::endl;
    system::cout << address0h_pub << std::endl;
    system::cout << address0h1_pub << std::endl;
    system::cout << address0h12h_pub << std::endl;
    system::cout << address0h12h2_pub << std::endl;
    system::cout << address0h12h2x_pub << std::endl;
    system::cout << address44h0h0h00_pub << std::endl;
    system::cout << std::endl;

    return EXIT_SUCCESS;
}
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commented

Thank you very much for adding the derivation example BIP44! Its matches the example of iancoleman.io Now I understand how derivation paths work.