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Bitcoin mnemonic private key consist of 12 words. Theese words represent private key.

I was thinking if it is possible to make it shorter than 12 by increasing set of words from which to choose. It would be easier to remember. Lets say we have set of 10000 words. How many words would be enough to represent one private key then? Does somebody know the exact calculation? Or any suggestion why this is not a good idea?

Thank you.

Martin Lipták
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  • Seed phrase info and calcs - https://en.bitcoin.it/wiki/Seed_phrase . Unless you are cryptography expert probably a bad idea to mess with these things :) – Matthew Page Jan 30 '19 at 23:39
  • The calculation is not difficult. If log(z, b) is the log to the base b of z, then the number of words you need to randomly select from a dictionary of N words is about 128* log(2, N). You should round up, or take the ceiling function, of the result. For your example with N=10000, this would give 10 words. This is assuming you want about 128 bits of security. – President James K. Polk Jan 31 '19 at 00:18
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    This is not a programming question. You may be able to get help at [bitcoin.se]. – Michael Hampton Jan 31 '19 at 02:11

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The seed phrase can contain any number of words that you want it to. Their function is simply to allow recreation of the private key for the Bitcoin wallet.

Regarding the length of 12 words, taken from here:

The English-language wordlist for the BIP39 standard has 2048 words, so if the phrase contained only 12 random words, the number of possible combinations would be 2048^12 = 2^132 and the phrase would have 132 bits of security. However, some of the data in a BIP39 phrase is not random, so the actual security of a 12-word BIP39 seed phrase is only 128 bits. This is approximately the same strength as all Bitcoin private keys, so most experts consider it to be sufficiently secure.

So although 12 would seem the correct amount, the important thing about them is that they must be securely stored, preferably in memory, but at least written and locked somewhere safe, and never stored in plaintext online or on your PC\devices.

One afterthought - by increasing the number of words that are used in the phrase, you could actually make it less secure because the longer it is, the more certain it would be that it must be recored somewhere physical rather than in your own memory.

Martin
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