Assume that I have a 24-word passphrase that I want to store securely but online by mixing it with another 24 words in a manner only I know. Does the checksum property somehow help an attacker to significantly speed up the process of guessing the right 24-word phrase in a reasonable time?
I would guess no because the attacker still needs to try an absurd number of combinations being somewhere in the vicinity of
$$ \binom{48}{24} \cdot 24! \approx 2 \cdot 10^{37}. $$
Edit: For clarifaction, I add a minimal example which led me to the above question. Let us consider the following simple passphrase system:
- Choose 3 distinct words from all words which can be set together by 3 letters (abc, god, ced, ....)
- The fourth word must fulfil that it contains the first letters of the three first words (that is meant to be a very simplified checksum condition)
Let us say I have the passphrase (ago, bro, sis, abs) and mix it with another passphrase (gro, lab, for, glf) to
(ago, glf, for, sis, abs, gro, lab, bro)
Now it is way faster to scan this sequence and check for which quadruple rule 2. applies to obtain the two possible valid pass phrases than just trying all $$ \binom{8}{4}\cdot 4! = 1680 $$ combinations.