Edit: Oops, as dpark points out, I swapped two digits. My apologies. Below, my original, erroneous comment.
41 bits of entropy means you have on the order of a one in 10^12 chance (2^41) of guessing it, and 2,000^4 is on the order of 10^16. So how is the former "one eighth as secure" as the other? Wouldn’t it be 10^4 times less secure, that is, 10,000 times more likely to be cracked?
41 bits of entropy means you have on the order of a one in 10^12 chance (2^41) of guessing it, and 2,000^4 is on the order of 10^16. So how is the former "one eighth as secure" as the other? Wouldn’t it be 10^4 times less secure, that is, 10,000 times more likely to be cracked?