First, all this is beside the point. Evernote hasn't understood the concepts of either entropy or human chosen passwords. Rejecting my passphrase and accepting "abc123" is wrong. That's my original post, and that's what you objected to. Computer generated random passwords that nobody's going to use on their mobile phone Evernote client, simply don't figure into normal human use.

Our job is to recommend things that can help real people use tech more safely.

> "the entropy of a randomly (not user!) selected password is not estimated in this manner, but calculated according to the same formula I provided: H = log_2 (b^L), where b is the number of letters in the alphabet (95) and L is the length of the password"

Yes, I'm aware of that. Using that site's check, "correct horse battery staple" comes out weaker at 104.2 bits, so I listed that weaker "lower bound"[1] for that phrase. I'm happy to use whatever formula comes up with less entropy for reasons discussed in [1].

I also don't care when sharing with less technical users if it's exact. I care if I can point them to a URL that gives a reasonable approximation, which that "quick check" does. For users who want to do math, I listed both approaches:

> 1. Quick entropy check: http://rumkin.com/tools/password/passchk.php

> 2. Manual entropy check: http://www.wolframalpha.com/input/?i=log_2%282048%5E4%29

The "manual" check is pre-filled with your suggested formula. It's interesting to compare the entropy check to http://www.passwordmeter.com which I think users will "solve" as if it were a password meter puzzle, in very predictable ways.

Meanwhile, to an attacker trying the whole character space, "correct horse battery staple" is log2(27^28) or 133.1 bits of entropy. And if you use H = log_2 (b^L) on the passphrase that Evernote wouldn't accept, it comes in at 188 bits of entropy.

In any case, the approximation is a more conservative "lower bound" than the formula you're suggesting as applied to character set ^ length.

> I personally think a password manager like keepass / lastpass / etc. is a better choice than trying to select a memorable password, though.

I agree. And I use 1Password and generate random passwords.

Btw, the two truly random passwords from 1Password (equivalent of keepass, lastpass, etc), if working with the H = log_2 (b^L) formula, give only 98 bits and 101 bits. Again in their case, the "quick entropy check" URL gives lower numbers, meaning it's a remains a reasonable "lower bound" check for casual users who don't grok formulas.

I tell non-technical family members and friends who can't be bothered with password minders to use sentences meaningful to them and unlikely to be in a book.

    This phrase is definitely not in the dictionary! : 227 bits or 286 bits

That's a pretty good password that my Mom can remember.

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1. lower bounds: http://subrabbit.wordpress.com/2011/08/26/how-much-entropy-i...