Kaju Yamaka • 05 de dez, 2019 (editado)

Bitcoin Proposal

Private Key to Mnemonic Words

Motivation

In the beginning of bitcoin (2009~2013), people created private keys by their own preferred random number generator. The most common ways were:

software
passphrase
rolling a dice
flipping a coin

Those more concerned with security recommended flipping a box full of coins and shake it very well to guarantee maximum entropy. The explanation at that time was quite reasonable:

Software randomness is not truly random and can be tampered by malicious attackers.
Choosing a strong passphrase in order to avoid brute force attacks can be very tricky. If you are able to memorize it, then most likely it is not as strong as you think.
It is common to see off the shelf dices with some bias.
"Physical randomness is better than computer generated pseudo-randomness."
BitAddress

However, storing these private keys in hexadecimal (or some compressed format) is very unfriendly. This motivated an improvement proposal in 2013, so that users could store seed phrases (24 easy to remember words from BIP39 wordlist) instead.

Unfortunately, soon after that, the industry standard quickly moved towards letting wallets automatically generate the private keys and users should only store the seed phrases in a safe place. The explanation given elsewhere in the web is that users are not reliable to generate randomness. Therefore, they should leave this task to the software. Which contradicts previous recommendations and even the core principal of bitcoin: trust no one.

Nowadays, if you want to create a private key by the old fashion way (but still very safe if done properly) like rolling a dice or flipping a coin, you will have a hard time looking for a software to automatically generate the seed phrase of such private key.

Therefore, this article simply tries to solve that by proposing such standard procedure.

Procedure

One way to create a seed phrase from a private key is to use the aforementioned BIP39 wordlist, which has 2048 (= 2¹¹) words, and map bits of the private key to the corresponding word.

However, 11 is not a multiple of 256. Therefore, it is necessary to split the 256 bits of the private key into 11-bit segments with padding/checksum appended to make it a multiple of 11. A reasonable way is to take the sha256 checksum of the private key and append the first 8 bits to get 264 bits. Which maps to 24 words.

In short, follow the steps below:

Sha256(pk)
Take the sha256 of the private key.
Append 8-bits
Take the first 8 bits of the sha256 calculate above and append to the private key.
You should get 264 bits.
Split into 11-bits
Split the 264 bits calculated above into 11 bits segments.
You should get 24 segments.
Map to Words
Map each 11 bits segment calculated above to the correspondent word from the BIP39 word list.

Example

Private Key:

Hexadecimal Format
8BFA0399016B9FCEE2F543F90701495583723D14E0C6A0AE69BF528CB4CB38C8

Binary Format
1000101111111010000000111001100100000001011010111001111111001110
1110001011110101010000111111100100000111000000010100100101010101
1000001101110010001111010001010011100000110001101010000010101110
0110100110111111010100101000110010110100110010110011100011001000

SHA256 of Private Key:

Hexadecimal Format
3BBE1C86172DB67C6E6261E1AE455AF02CF01C86CE538A81C1EB03C9CC73ED12

Binary Format
0011101110111110000111001000011000010111001011011011011001111100
0110111001100010011000011110000110101110010001010101101011110000
0010110011110000000111001000011011001110010100111000101010000001
1100000111101011000000111100100111001100011100111110110100010010

Private Key with 8 bits checksum appended:

1000101111111010000000111001100100000001011010111001111111001110
1110001011110101010000111111100100000111000000010100100101010101
1000001101110010001111010001010011100000110001101010000010101110
0110100110111111010100101000110010110100110010110011100011001000
00111011

11-bits segments with corresponding BIP39 word:

01    10001011111    1119    message
02    11010000000    1664    source
03    11100110010    1842    town
04    00000010110    0022    actress
05    10111001111    1487    rigid
06    11100111011    1851    trash
07    10001011110    1118    mesh
08    10101000011    1347    position
09    11111001000    1992    weekend
10    00111000000    0448    day
11    01010010010    0658    false
12    10101011000    1368    prison
13    00110111001    0441    damp
14    00011110100    0244    burden
15    01010011100    0668    fatal
16    00011000110    0198    boat
17    10100000101    1285    pass
18    01110011010    0922    infant
19    01101111110    0894    hurt
20    10100101000    1320    pink
21    11001011010    1626    slender
22    01100101100    0812    grain
23    11100011001    1817    tobacco
24    00000111011    0059    alter

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