We all know that with a 12, 18, or 24 word seed one can generate a Bitcoin wallet in an "address space" that is so large that it would be, essentially, impossible to guess. Right?
Right.
Does a 24 word seed phrase fully cover the entire "address space" such that if all combinations of seed words are used, all possible wallet addresses will be mapped / addressed?
Yes. Given 2
96 private keys per address, all addresses are covered billions times billions times billions of times.
What about passphrases? Does the use of a passphrase open up new "address space" or does it map to an address in the original address space, such that seed phrase X without a passphrase may map to (be equivalent to) seed phrase Y with passphrase Z? Or seed phrase M with passphrase N maps to seed phrase O with passphrase P?
And what about the following BIPs which talk about various forms of creating sub-accounts/sub-wallets based on a primary wallet seed? Do these result in "overlap" with the original 24 word "address space"?
Each 24 word seed with or without passphrase covers
all possible addresses. Think about what this means for a while, it's truly amazing.
--Knight Hider