Private Key Conversion
Writing down a binary private key accurately is difficult for humans, and entering it correctly into a wallet is even harder. A single mistake could lead to losing Bitcoin. While a computer can detect errors using a checksum, handwritten notes cannot.
Converting Binary to Decimal
One way to make private keys easier to write is by converting them from binary to decimal. If the binary is divided into 11-digit chunks, the largest possible value for each chunk is 2047 (since 11-bit binary numbers range from 00000000000 to 11111111111, which is 0 to 2047 in decimal).
This means a private key can be written as 24 groups of decimal numbers, each ranging from 0 to 2047. This format is easier to write but still prone to errors.
The BIP39 Solution: Using Words Instead of Numbers
To reduce errors, BIP39 introduced a method where each decimal number is replaced with a word from a fixed list of 2048 words. These words were carefully selected to minimize misinterpretation. The list is available in multiple languages, and each word corresponds to a number from 0 to 2047.
Using words instead of numbers is how seed phrases work. When you enter a seed phrase into a wallet, the software converts each word back into an 11-digit binary number, then combines them all into a 264-bit binary private key (for a 24-word phrase). The last word includes checksum bits, so it is not fully random. A 12-word seed phrase follows the same process but results in a 132-bit private key instead.
A Formatting Issue in the BIP39 Word List
The official BIP39 word list is stored on GitHub, where words are numbered from 1 to 2048 instead of 0 to 2047. This is just a formatting issue, but it can be confusing.
For example, if the private key starts with 00000000000 (binary zero), the corresponding word should be the first word on the list, which is "abandon." However, on GitHub, "abandon" is labeled as word 1 instead of 0. This means every word in the list appears one position higher than the number it actually represents, requiring a simple correction when looking up words.
Step-by-Step Conversion Example
Consider this binary private key (with the last 8 digits generated as a checksum):
101110001011101110010010111100111011010001011111101010111111001000001000001011011100010110101010100101110111011111100010101111001110101110101001001100011110111000111111110111010001100010110101000110111110101001111100010000101000101101110101011001100010100101010010
Step 1: Break into 11-digit chunks
10111000101 11011100100 10111100111 01101000101 11111010101 11111001000 00100000101 10111000101 10101010100 10111011101 11111000101 01111001110 10111010100 10011000111 10111000111 11111011101 00011000101 10101000110 11111010100 11111000100 00101000101 10111010101 10011000101 00101010010
Step 2: Convert each chunk to decimal
1477, 1764, 1511, 837, 2005, 1992, 261, 1477, 1364, 1501, 1989, 974, 1492, 1223, 1479, 2013, 197, 1350, 2004, 1988, 325, 1493, 1221, 338
Step 3: Look up words in the BIP39 list
Each decimal number corresponds to a word in the official BIP39 word list. However, since the GitHub list starts from 1 instead of 0, we must subtract 1 from each number before looking up the word.
For example:
- 1477 corresponds to word 1478 in the GitHub list, which is "reward".
- 1764 corresponds to word 1765 in the GitHub list, which is,"symptom", and so on.
Final Word List:
reward symptom rude hamster wide weekend camera reward pride roof weather keep ritual ocean rib wing board potato whisper weasel chunk rival obvious clean
Observing the Word Order
The words are arranged in alphabetical order, meaning words that start with A represent lower numbers, and words near the end of the list represent higher numbers. This ordering becomes more obvious once you understand how the BIP39 system works.
Using words instead of numbers makes writing down a private key much easier and reduces errors. This system is why most wallets use seed phrases rather than raw binary or decimal keys.
Conclusions
To summarize, we’ve explored how a seed phrase originates from a private key, which itself is simply a very large random number.
What is a Seed Phrase?
A seed phrase is a series of 12 or 24 words that act as a backup for your Bitcoin wallet's private key. It’s a human-readable way to store and recover your private key, which controls access to your Bitcoin. The seed phrase is generated when you create a Bitcoin wallet and can be used to restore your wallet if you lose your device or need to set it up again.
How Does a Seed Phrase Work?
The seed phrase is based on the BIP39 standard, which means that these 12 or 24 words are not random but follow a specific order and dictionary. These words are generated from a list of 2048 words, and as long as you have the correct set of words in the correct order, you can recreate your private key and access your funds.
Because the seed phrase is tied to your private key, whoever has access to it can control your Bitcoin. Therefore, keeping it secure is critical.
Why is a Seed Phrase Important?
A seed phrase allows you to back up your Bitcoin wallet in a secure, easy-to-remember way. Instead of storing a long private key, you can simply write down the seed phrase on paper or store it in a secure digital form. If your device is lost, stolen, or damaged, you can restore your Bitcoin wallet by entering the seed phrase into a new wallet app or hardware wallet.
In a sense, your seed phrase becomes your wallet’s master key. It’s also far more practical to store 12 or 24 words than to store a complex, long private key.
Create your Seed Phrase
If you feel to go deep down the Seed Phrase rabbit hole, I highly recommend to create your own seed phrase generating a true entropy
This the guide link