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by rcoveson 1044 days ago
The thing about the Lord's Prayer doesn't really follow. If you use a grammatically correct and semantically commonplace 12 word sequence like that, you surely don't have 128 bits of entropy. But the ease of memorization comes almost entirely from those attributes!

To get 128 bits of entropy with words, you need to pick about thirteen out of a million words--which is on the order of all the words in the English language--and give all of them equal probability. The sequence needs to be fully random as well. What you end up with will surely be easier to memorize than a UUID, but substantially more difficult than the start of the Lord's Prayer.

EDIT: Math is wrong, I was thinking 10 bits per million instead of 20. So 6-7 words out of a million (whole language) or 13 words out of a thousand (very limited subset of the language). Point about random selection still stands, but it's certainly easier than 13 very uncommon words. Still much harder than a realistic sentence of that length, though.