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(We really should just have a button to link this XKCD)

I've just started switching my passwords into passphrases. Now, I didn't roll any dice to come up with them, which I know sacrifices entropy; they're sentences. They're at least 25 characters long, at least 5 words, and I try to slip a number in there as well as a "fake" word (this would be either a bastardization of a word I make up or a non-standard word like "doggo" or "borked").

Now, I know the fact that I have a structure at all means I've lost potential entropy, but the message I got away from that XKCD is that memorizablity is a resource to be maximized as well as entropy. I appreciate that I can tell my wife these passwords without needing to ever write them down (or, god forbid, text/email them). I hope to never actually see an active password of mine.

My question, then, is Am I likely to see any practical increase in security by combining passphrases and leetspeak?

"Practical increase in security" here means additional protection from any attack vectors given modern hardware in a reasonable time period. I know leet-speak would obviously help, but if an attack on the passphrase alone is infeasible, I'd rather not complicate my password. This is in the average case; I'm not concerned with someone dedicating dozens of GPUs to my password alone for months on end.

You can make the assumption any changes would be easily memorized. I'm mostly curious if a passphrase provides enough entropy on its own that the traditional strategies for entropy are no longer relevant. As an example, is the second password here pragmatically any better than the first?

mydoggoShrekate7bonesyesterday
myd0ggoShr3k4te7bon3$yesterd@y

(Also, please don't just suggest a password manager. I have my reasons for wanting to avoid one.)

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    yes, it's better. brute-forces can consume word lists, which basically makes each word cost a character. others can do leet substitutions words, but at a greatly reduce speed than plain. Putting them together moves a lot of math into your favor, much more than either approach alone. – dandavis Jul 18 '18 at 16:06
  • @dandavis I know it's better, but I'm wondering if it's pragmatically better. As in, is a lengthy enough passphrase strong enough already. If I just wanted the best password possible I'd randomly generate the longest password each site took, but I'm hoping to make a trivially memorizable password that still crosses the "good enough" security threshold. Also, words don't quite cost a character, as there are 62 alphanumerics (looks like my keyboard has just over 90 characters total), but thousands of words. – Lord Farquaad Jul 18 '18 at 16:39
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    @dandavis well sure, but the password "password" is objectively bad, while a random 25 char password is objectively good. Does this fall in the gray area in-between? – Lord Farquaad Jul 18 '18 at 16:48
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    i think both your scheme and a random 25 fall under into "not going to happen with affordable hardware in a reasonable time" bucket – dandavis Jul 18 '18 at 16:52
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    The XKCD comic you link very specifically relies on randomly selecting the words. If you don't randomly select the words the whole analysis is wrong. Did you at least make up your own sentences rather than pulling quotes from somewhere? Also, use a password manager. Your reasons are probably misguided. There are some reason not to use one but they tend to be in specialized circumstances (like being legally barred from storing your password to a high-security area for example). – Ben Jul 18 '18 at 16:54
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If memorability and readability is your goal, then the second version of your password (that is: myd0ggoShr3k4te7bon3$yesterd@y) is much more difficult to memorize, read, and communicate. So yes, it will definitely hamper and slow down most bruteforcing attempts based on word lists, but at the expense of memorability and readability.

It's hard to calculate the entropy of your password. I'm not sure I'm able to do it, but I'll try anyway, and if I'm wrong somebody will correct me.

If you google for "entropy of English sentence", you can find some articles citing Shannon's experiment to calculate the entropy of English. From what I read, it seems that on average the entropy can go from 0.6 bits to 2.5 bits per letter, depending on a lot of factors. Let's suppose your sentence has 1.5 bits per character. Some letters will have higher entropy because of your made-up words, other letters will have a lower entropy because they are part of very basic English words, so let's suppose on average it's 1.5 bits per character anyway.

30 characters x 1.5 bits = 45 bits

Now let's transform the pass phrase. For simplicity, we suppose we basically need to pick 7 letters and translate them to leet. Supposing only half of the letters have a leet equivalent, we need to pick 7 letters out of 15. And we need combinatorics, which if I'm not wrong (it's been a long time since math classes, sigh) leads to this:

15! / (7! (15-7)!) = 6435 possible groups of leet letters.

So to guess your leet password all those possibilities need to be bruteforced for each sentence, meaning that will add 12.65 bits of entropy (that is, log base 2 of 6435). It's a rough estimate, for example I didn't consider the fact that "a" in leet can be either "@" or "4", but I just assumed that every translatable letter could be translated to only one equivalent.

So, to recap, if I'm not wrong, and in an ideal world where the attacker knows how you build your passwords and where password crackers are optimized for the entropy of the English language instead of just bruteforcing ungrammatical bunches of words, we have the following entropies:

30-character sentence: 45 bits
30-character leet sentence: 57.65 bits
40-character sentence: 1.5 x 40 = 60 bits
5-word diceware pass phrase (about 30 characters) = 12.9 x 5 = 64.5 bits

Conclusion: I'd suggest using a longer sentence or better yet a true random pass phrase like diceware or similar, so you can easily achieve both higher entropy and at the same time readability and memorability.

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    +1. Adding a random word or two is always better than adding complexity elsewhere. – Royce Williams Jul 18 '18 at 18:51

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