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Why 18 words are ideal for singlesig wallets

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I think most people use 24 words today, which is just plain unneccessary. And I don't mean unneccessary due to 12 words being safe enough, but because modern (P2WPKH) singlesig addresses are only 160 bits long. Thus, 96 of the 256 bits of entropy forming a 24 word mnemonic are just there to make your life of storing the mnemonic more difficult without enhancing the wallets security.

There are also 15 word mnemonics. Those are generated from exactly 160 bits of entropy. This may seem perfect at first. But this is only the case, if you have a perfect source of entropy, e.g. a perfectly fair dice (with completely decoupled rolls).

So, let me introduce the 18 word mnemonic: It is created from 192 bits of entropy. First off, this is more than 160 bits, so already enough if you have a perfect entropy source. However the additional 32 bits of cushion even allow you to use non-perfect entropy sources and still be sure to still have more than 160 bits of randomness. Example: Rolling 192 bits with a perfect dice takes 74 rolls. Now, imagine your dice is very bad and never shows a "six" with the remaining results being equally probable. Even then, rolling 74 times you still have 172 bits of entropy.

TLDR: P2WPKH addresses are only 160 bits long. 18 words are perfect to generate such long addresses with an additional cushion to straighten out somewhat bad entropy sources.

PS: 12-word maxis, please don't lynch me. I know 12 words are usually considered enough, but why not go for 18, just 6 more, and you have the highest entropy possible with P2WPKH addresses?

submitted by /u/theyseemestackin
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