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Recovering-Your-Keys-Without-the-MMGen-Software.md

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Table of Contents

Introduction

If you’re considering using MMGen and are a Bitcoiner with a normal, healthy degree of paranoia, then the following question will probably come to mind: “What if I have funds in an MMGen wallet and I lose the software? How do I recover my coins?”

Let’s take this scenario to its logical extreme and assume you’ve lost all backup copies of the software, MMGen’s project page has disappeared from both Github and Gitlab (or been hacked) and no other repositories or copies are available on the Internet. The following tutorial will show you how to recover the private keys for your coin addresses in the event this unlikely combination of circumstances ever occurs.

In addition to private keys, this tutorial can also be used to recover passwords generated with the mmgen-passgen command.

Obtaining the binary seed

To keep things simple, we’ll assume you have a copy of your seed in hexadecimal (mmhex) format. If your backup’s in mnemonic format, skip to the section Converting an MMGen mnemonic to hexadecimal format below and return here when you’ve finished. If your backup is an MMGen wallet, it will need to be decrypted. That case will be covered in a future tutorial.

Okay, so let’s say you have a 128-bit seed with Seed ID FE3C6545 and funds in the first three legacy uncompressed (L) addresses of this seed. Here are the addresses:

FE3C6545 {
  1   1JVi3qcNcjMM7cTR7y9ihKUG1yDLpKRJfL
  2   15EfKymfe3v7mqCaL174hTWSgBLFAHvtaR
  3   1CUDd6nPHdP5pT7nN8k2AA5WdKRaKPjmea
}

Since you might have your funds in Segwit (S) addresses, we’ll consider that case too:

FE3C6545 SEGWIT {
  1  3LpkKqtGkcCukRrgEFWyCajSApioiEWeTw
  2  3FYZQyWqBJcCjaSjCV9ZVj3gKyB9u8AYCX
  3  37wM8hwt69qwH7hZHAMn6RVdc8vMuM1CwJ
}

Keys for compressed (C), Bech32 (B) and altcoin addresses, as well as passwords, are generated in a way analogous to Segwit keys, so for them you’ll proceed as with the Segwit case.

Here’s the seed itself in mmhex format, which you’ve stored in some safe place (on paper in a safe-deposit box, for example):

afc3fe 456d 7f5f 1c4b fe3b c916 b875 60ae 6a3e

Now your task is to generate keys for the addresses so you can spend your coins. This task is divided into two parts:

  1. generating the keys and converting them to hexadecimal format; and
  2. converting the hex keys to wallet interchange (WIF) format for importation into Bitcoin Core or some other wallet.

We’ll solve this task using standard command-line utilities available on any Linux or other Unix-like system.

Convert the seed to binary (legacy uncompressed addresses)

For the legacy addresses, we begin by converting the seed to binary form and storing it in a file. For that we use xxd, a handy tool for converting binary to hex and vice versa. Don’t forget to omit the checksum from the seed and remove the spaces:

$ echo 456d7f5f1c4bfe3bc916b87560ae6a3e | xxd -r -p > myseed.bin

Scramble the seed and save to binary (non-legacy and altcoin addresses and passwords)

Other address types and passwords are generated by first “scrambling” the seed with a unique identifier, or “scramble string”, using the HMAC-SHA256 algorithm. The scrambled seed is then given ten rounds of SHA256 to create the base seed used to generate our keys.

Our first task then is to find out the correct scramble string for our coin and address type (or password). For BTC and BTC fork coins, the string will be simply the address type, e.g. compressed or segwit. For Bitcoin-based altcoins, the string is the coin symbol and address type separated by a colon, e.g. ltc:legacy. The strings for non-Bitcoin-derived altcoins are irregular and are listed in the table below. For passwords, the string is the password format, e.g. b58; the password length, e.g. 20; and the password ID string, e.g. alice@fubar.io, all separated by colons:

Coin + Address type Scramble String
BTC/BCH compressed compressed
BTC Segwit-P2SH segwit
BTC native Segwit (Bech32) bech32
LTC legacy ltc:legacy
LTC compressed ltc:compressed
LTC Segwit ltc:segwit
LTC Bech32 ltc:bech32
DASH legacy dash:legacy
DASH compressed dash:compressed
ETH eth
ETC etc
XMR xmr:monero
ZEC-T zec:legacy
ZEC-Z zec:zcash_z
Password type Scramble String
Base58 passwords for Alice’s email acct. b58:20:alice@fubar.io
Same as above, half-length passwords b58:10:alice@fubar.io
Same as above, default Base32 passwords b32:24:alice@fubar.io
32-byte hex seed for Alice’s PGP key hex:64:alice@gnupg

Once we’ve determined the correct string, we scramble our seed with it as follows using the openssl utility available by default on any Unix-based system:

# e.g. for LTC Segwit addresses:
$ scramble_str='ltc:segwit'

# e.g. for default-format passwords for Alice’s email account at fubar.io:
$ scramble_str='b58:20:alice@fubar.io'

$ echo -n "$scramble_str" | openssl dgst -r -sha256 -mac hmac -macopt hexkey:456d7f5f1c4bfe3bc916b87560ae6a3e | xxd -r -p > scrambled-round0.bin

Now add the ten rounds of sha256:

$ for i in 0 1 2 3 4 5 6 7 8 9; do
      openssl dgst -sha256 -binary scrambled-round${i}.bin > scrambled-round$((i+1)).bin
  done

$ mv scrambled-round10.bin myseed.bin

Generating the keys

The MMGen key-generating algorithm uses a chain of SHA-512 hashes with double SHA-256 branches to generate the keys from which each address is derived. To obtain the chain’s first link, we make a single SHA-512 hash of the seed and save it in binary form:

$ sha512sum myseed.bin | xxd -r -p > link1.bin

A double SHA-256 hash of the first link gives us the key of our first address:

$ sha256sum link1.bin | xxd -r -p | sha256sum
05d7219524b983290138a60ada101370007f59a625c43a46f0f8d92950955e36

Or, for the Segwit example:

b8e58ded53e9ba5a9f4e279a956c061a7da5487bde6a95f1ede0722d287881a0

Or, for the password example:

bd60b8ba034bbb40498667ee600bc0cc0b99eb19164e8d412a48f16da4e00d6b

Checking the result (optional, address example)

With mmgen-tool, we can easily generate the WIF key and address from this hexadecimal key and see that it’s correct:

$ mmgen-tool hex2wif 05d7219524b983290138a60ada101370007f59a625c43a46f0f8d92950955e36
5HrrmMdQbELyW7iCns5kvSbN9GCPTqEfG7iP1PZiYk49yDDivTi

$ mmgen-tool wif2addr 5HrrmMdQbELyW7iCns5kvSbN9GCPTqEfG7iP1PZiYk49yDDivTi
1JVi3qcNcjMM7cTR7y9ihKUG1yDLpKRJfL # matches FE3C6545:L:1 above

Or, for the Segwit example:

$ mmgen-tool hex2wif b8e58ded53e9ba5a9f4e279a956c061a7da5487bde6a95f1ede0722d287881a0 compressed=1
L3R8Fn21PsY3PWgT8BMggFwXswA2EZntwEGFS5mfDJpSiLq29a9F

# for a compressed (`C`) address, leave out the `segwit=1` argument
$ mmgen-tool wif2addr L3R8Fn21PsY3PWgT8BMggFwXswA2EZntwEGFS5mfDJpSiLq29a9F segwit=1
3LpkKqtGkcCukRrgEFWyCajSApioiEWeTw # matches FE3C6545:S:1 above

But since we’re trying to do this without the MMGen software, we need to find some other way to do the hex-to-WIF conversion. We could use one of many key-manipulation tools available on the Internet, such as this one, or this one. Or we can do it ourselves: that will be covered in the next section.

Meanwhile, let’s finish generating hex keys for the rest of our addresses (or passwords). To get the next key, we generate the next link in the chain from the first link and take its double SHA-256 hash, just as we did for the first one:

$ sha512sum link1.bin | xxd -r -p > link2.bin

$ sha256sum link2.bin | xxd -r -p | sha256sum
5db8fe3c8b52ccc98deab5afae780b6fbe56629e7ee1c6ed826fc2d6a81fb144 # uncompressed example
42f1b998f0f9b7b27b5d0b92ffa8c1c6b96d7202789c41b6e6a6a402e318a04d # Segwit example
9b59cec2e5d4f2a74f0d4eb2400efcf854f5a893bef0e9bf1ee83f72ca1118c3 # password example

And so on and so forth, until we’ve generated all the keys we need: three, in our case.

If we’re generating keys for Ethereum and Monero, our work is done: the raw hexadecimal keys are all we need. Otherwise, read on.

Converting the hex value to a password (password example)

If it’s passwords we’re generating, we must now convert our hex key to the desired password format, base58 in our case. For this we can use the homemade hex2b58.py Base-conversion utility described below:

# bd60b8... is the double sha256 of our link1.bin from above
$ ./hex2b58.py bd60b8ba034bbb40498667ee600bc0cc0b99eb19164e8d412a48f16da4e00d6b
DkFbZk2fDKQ7C55ASHQjhwcCdTsCiRq4ZLMMD5WQVAvv

The password is just the last 20 characters of the output:

dTsCiRq4ZLMMD5WQVAvv

Hex to WIF by hand (address example)

Since we’ve chosen to convert our hex keys to WIF format manually, we have a bit of work ahead of us. Let’s begin with our just-generated key #1 from seed FE3C6545:

# uncompressed example
05d7219524b983290138a60ada101370007f59a625c43a46f0f8d92950955e36

# Segwit example
b8e58ded53e9ba5a9f4e279a956c061a7da5487bde6a95f1ede0722d287881a0

WIF format prepends hex 80 to the beginning of the key. If the key is associated with a compressed public key, it also appends 01:

# uncompressed example:
8005d7219524b983290138a60ada101370007f59a625c43a46f0f8d92950955e36

# Segwit example (Segwit uses compressed public keys):
80b8e58ded53e9ba5a9f4e279a956c061a7da5487bde6a95f1ede0722d287881a001

The Base58Check format invented by Satoshi for Bitcoin addresses and keys contains a checksum, which we now generate by taking the first four bytes (eight characters) of the double SHA256 of the above result:

# uncompressed example:
$ echo 8005d7219524b983290138a60ada101370007f59a625c43a46f0f8d92950955e36 | xxd -r -p | sha256sum | xxd -r -p | sha256sum | cut -c 1-8
7b818629

# Segwit example:
$ echo 80b8e58ded53e9ba5a9f4e279a956c061a7da5487bde6a95f1ede0722d287881a001 | xxd -r -p | sha256sum | xxd -r -p | sha256sum | cut -c 1-8
89bba812

The checksum gets appended to the end, giving us the following final result:

# uncompressed example
8005d7219524b983290138a60ada101370007f59a625c43a46f0f8d92950955e367b818629

# Segwit example
80b8e58ded53e9ba5a9f4e279a956c061a7da5487bde6a95f1ede0722d287881a00189bba812

The last step is to convert all this into Base 58. Satoshi created Base-58 encoding for convenient and error-free writing down and dictating of Bitcoin keys and addresses. He began with a Base-62 alphabet consisting of the ten digits plus the upper and lower case Latin letters (10 + 26 + 26 = 62):

0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijlkmnopqrstuvwxyz

Since ‘0’ (zero) is easily confused with capital ‘O’ visually, and capital ‘I’ with lowercase ‘l’, he dropped those characters, leaving the following 58:

123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz

With ‘0’ gone, ‘1’ now represents decimal zero, ‘2’ represents decimal one, and so forth all the way up to ‘z’, representing decimal fifty-seven.

Now all that remains is to convert our hexadecimal key to decimal and then Base 58 using this alphabet. This can be done in just four lines of code you can try out at the Python prompt:

# uncompressed example:
$ python3
>>> b58a = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
>>> num = int('8005d7219524b983290138a60ada101370007f59a625c43a46f0f8d92950955e367b818629',16)
>>> result = [b58a[num // 58**e % 58] for e in range(60)]
>>> print(''.join(reversed(result)).lstrip('1'))
5HrrmMdQbELyW7iCns5kvSbN9GCPTqEfG7iP1PZiYk49yDDivTi # matches key for FE3C6545:L:1 above

# Segwit example has the following differences:
...
>>> num = int('80b8e58ded53e9ba5a9f4e279a956c061a7da5487bde6a95f1ede0722d287881a00189bba812',16)
...
L3R8Fn21PsY3PWgT8BMggFwXswA2EZntwEGFS5mfDJpSiLq29a9F # matches key for FE3C6545:S:1 above

Explanation: the variable b58a holds the Base 58 alphabet; num holds the key in decimal, converted from hexadecimal by Python’s int() function; the third line does the base-58 conversion; and the last line formats the result by reversing the order of the digits, converting it to a string and stripping off the leading zeroes (‘1’s).

Programmers unfamiliar with Python might find the following base conversion code clearer:

def numtob58(n):
	result = []
	while n:
		result = result + [b58a[n % 58]] # divide n by 58 and take the remainder
		n = n // 58
	return result

result = numtob58(num)

Base-conversion utility

Adapting our code a bit and putting it in a file gives us have a handy conversion utility we can use for any key:

$ cat hex2b58.py
#!/usr/bin/env python3
import sys
b58a = '123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz'
num = int(sys.argv[1],16)
result = [b58a[num // 58**e % 58] for e in range(60)]
print(''.join(reversed(result)).lstrip('1'))

$ ./hex2b58.py 8005d7219524b983290138a60ada101370007f59a625c43a46f0f8d92950955e367b818629
5HrrmMdQbELyW7iCns5kvSbN9GCPTqEfG7iP1PZiYk49yDDivTi

$ ./hex2b58.py 80b8e58ded53e9ba5a9f4e279a956c061a7da5487bde6a95f1ede0722d287881a00189bba812
L3R8Fn21PsY3PWgT8BMggFwXswA2EZntwEGFS5mfDJpSiLq29a9F

Converting an MMGen mnemonic to hexadecimal format

Our familiar base-10 system uses a series of ten symbols known as digits to represent numbers from zero to nine:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

If a number has more than one digit, its value is the sum of its digits multiplied by increasing powers of ten, beginning with the rightmost, least significant digit (the “ones column”).

Thus the number 1234, for example, can be represented as follows:

4 x 1 +
3 x 10 +
2 x 100 +
1 x 1000

Or in exponential notation:

4 x 10⁰ +
3 x 10¹ +
2 x 10² +
1 x 10³

An MMGen seed mnemonic is a number too, only the “digits” it’s comprised of come from an alphabetically sorted series of 1626 words, the Electrum wordlist, which begins like this:

able (0), about (1), above (2), abuse (3), accept (4) ...

and ends like this:

yet (1621), young (1622), yours (1623), yourself (1624), youth (1625)

(Type mmgen-tool mn_printlist enum=true to see the full enumerated list)

The words of the Electrum wordlist thus make up a base-1626 numbering system, just like the ten digits of our familiar base-10 system.

Here’s the mnemonic of our seed FE3C6545:

dude foot desperate tie stood themselves trip descend cease suicide apple busy

To decode it, we begin by listing its words, from least to most significant, along with the value of each word corresponding to its position in the wordlist:

busy       - 200
apple      - 59
suicide    - 1384
cease      - 221
descend    - 379
trip       - 1493
themselves - 1433
stood      - 1348
tie        - 1459
desperate  - 386
foot       - 562
dude       - 439

All that remains is to multiply the values by increasing powers of the base and sum the results, just as we did in our ‘1234’ example above:

200  x 1626⁰ +
59   x 1626¹ +
1384 x 1626² +
221  x 1626³ +
379  x 1626⁴ +
1493 x 1626⁵ +
1433 x 1626⁶ +
1348 x 1626⁷ +
1459 x 1626⁸ +
386  x 1626⁹ +
562  x 1626¹⁰ +
439  x 1626¹¹

While we could theoretically do the math with a calculator, a few lines of Python will make our work much easier:

$ python3
>>> sum = exp = 0
>>> for word in (200,59,1384,221,379,1493,1433,1348,1459,386,562,439):
>>> 	sum += word * 1626 ** exp
>>> 	exp += 1
>>> print(hex(sum))
0x456d7f5f1c4bfe3bc916b87560ae6a3e # the result in hexadecimal: matches our original hex seed above

In case you’re wondering why 1626 was chosen as the base: 1626 is just large enough to allow a 128-bit seed to be represented by twelve words. This can also be demonstrated at the Python prompt:

$ python3
>>> 1626**12 >= 2**128
True
>>> 1625**12 >= 2**128
False