Hi everyone.
I have a question.
The BIP39 provides the word list in many languages, right? (see
https://github.com/bitcoin/bips/blob/master/bip-0039/bip-0039-wordlists.md)
There are just 2048 records.
However, English has more than 20.000 words (ChatGPT says around 30.000.....).
My question is:
In the future, can the entire word list be completely replaced by a more comprehensive and agreed-upon BIP?
Or is it mathematically impossible to proceed with that substitution?Thank you in advance
Hi.
Let's examine how BIP39 works.
So, your device generates 128 bits of entropy (assuming you want 12 words seed phrase). Then the entropy looks like this:
10001001011110001...001
Then the entropy is hashed with SHA256. From the output, you will hold only the first 4 bits.
So now you have 128 bits of entropy + 4 bits that are called "checksum".
We will split these 132 bits into 12 segments of 11-bits each.
Imagine something like:
10001001011
11000100100
...
01000100001
Now we will convert those binaries to decimals:
1099
1572
...
545
Let's go to the BIP39 wordlist and check where these numbers correspond to:
matter
settle
...
dune
Now, following this process you realise that the max decimal you can get with 11 bits is 2047 (index starts at 0). So the max number of words you can have is 2048.
What would be needed if we wanted more words? Larger initial entropy (more bits) or the same amount of bits but less segments to be split into.
Is it necessary, or is it better? No! the fact that your seed phrase is selected from a set of 2048 words makes it super secure, so anything higher is an overkill.
But, higher entropy doesn't mean more secure? Yes, it does, but when we talk about bitcoin private keys, you can only get a maximum of 128 bits of security. This means that even if you create an entropy of 2000 bits to produce a private key, there can be someone who will generate the same key by solving the ECDSA algorithm, without messing with the size of the seed phrase at all.
Therefore, I believe there is no need for larger seed phrases or more english words in them. We must focus on securing the backups properly and not on trying to increase security in this regard.