5 ms·

I think XKCD is correct here. If you choose four random words from a list of 2048 common words, and your attacker knows that's what you're doing, then your en

I think XKCD is correct here. If you choose four random words from a list of 2048 common words, and your attacker knows that's what you're doing, then your entropy is 4 * log_2(2048) = 44 bits. If the attacker didn't know your strategy and tried to brute force letter by letter it would be much higher - around 48log_2(26)=150 bits assuming around eight letters per word - but like you said, we should assume the attacker knows exactly what strategy we're using, so 44 bits is the better number to work with. Since that's still more than 28 bits, a 'correct horse battery staple' type password is harder to crack then a short random string of mixed characters, even if the attacker knows exactly what your password generation strategy is.

whiteandnerdy 10y ago
> I think XKCD is correct here. > If you choose four random words from a list of 2048 common words, and your attacker knows that's what you're doing, then your entropy is 4 * log_2(2048) = 44 bits. If the attacker didn't know your strategy and tried to brute force letter by letter it would be much higher - around 48log_2(26)=150 bits assuming around eight letters per word - but like you said, we should assume the attacker knows exactly what strategy we're using, so 44 bits is the better number to work with. > Since that's still more than 28 bits, a 'correct horse battery staple' type password is harder to crack then a short random string of mixed characters, even if the attacker knows exactly what your password generation strategy is. Typo in the above but can't edit on my phone, the second sum should be 4 \* 8 \* log_2(26). Apologies.
hvidgaard 10y ago
Can we really assume 2048 different words? 100 words make up 50% of all words written according to this https://en.wikipedia.org/wiki/Most_common_words_in_English https://en.wikipedia.org/wiki/Most_common_words_in_English ? I was a bit hasty of the entropy of the passphrase, my mistake. I still stand by that even if we choose from 2048 common words, generating a good passphrase (one that isn't a common sentence) is harder than we think.
- oneeyedpigeon 10y ago
  None of [ "correct", "horse", "battery", "staple" ] are in that 100 list, though.
- croon 10y ago
  I'd go so far as to say that 2048 words aren't that many. Here's Merriam-Websters 3000 _core_ words [1]. Here's a list of 355k words [2]. [1] http://learnersdictionary.com/3000-words http://learnersdictionary.com/3000-words [2] https://github.com/dwyl/english-words https://github.com/dwyl/english-words
  - hvidgaard 10y ago
    There is not 3000 _core_ words. You don't teach elementary school children 3000 words. That list is significanly smaller. In Denmark it's 120 words, then you'll be well on your way to reading and writing most basic stuff. That someone has selected 2048 words used to generate passphrases, doesn't make it easy to remember.
    - rsanders 10y ago
      I've been doing this for years and it is indeed easier to remember. You won't be keeping all your passwords in your head in any format if you're using a unique password per site or service as you should. But you occasionally have to buffer them mentally between your password manager and the input box (especially on mobile), and the same number of bits of entropy are infinitely easier to copy correctly in this format vs something like "?G[G6n|4".
    - aangjie 10y ago
      Err.. I would suspect most(non-english?) people on the internet to know 2000 words. (By virtue of being atleast bi-lingual, they would, so the challenge boils down to can they type it? unicode support should help, but I've found most cases people simply type those sounds in English.) As for the English as a primary language people, I've no clue about the number of words, but if we can expect them to type 1024 words, we'd still get 20 bits..

whiteandnerdy 10y ago

> I think XKCD is correct here. > If you choose four random words from a list of 2048 common words, and your attacker knows that's what you're doing, then your entropy is 4 * log_2(2048) = 44 bits. If the attacker didn't know your strategy and tried to brute force letter by letter it would be much higher - around 48log_2(26)=150 bits assuming around eight letters per word - but like you said, we should assume the attacker knows exactly what strategy we're using, so 44 bits is the better number to work with. > Since that's still more than 28 bits, a 'correct horse battery staple' type password is harder to crack then a short random string of mixed characters, even if the attacker knows exactly what your password generation strategy is. Typo in the above but can't edit on my phone, the second sum should be 4 \* 8 \* log_2(26). Apologies.

hvidgaard 10y ago

Can we really assume 2048 different words? 100 words make up 50% of all words written according to this https://en.wikipedia.org/wiki/Most_common_words_in_English https://en.wikipedia.org/wiki/Most_common_words_in_English ? I was a bit hasty of the entropy of the passphrase, my mistake. I still stand by that even if we choose from 2048 common words, generating a good passphrase (one that isn't a common sentence) is harder than we think.

oneeyedpigeon 10y ago
None of [ "correct", "horse", "battery", "staple" ] are in that 100 list, though.
croon 10y ago
I'd go so far as to say that 2048 words aren't that many. Here's Merriam-Websters 3000 _core_ words [1]. Here's a list of 355k words [2]. [1] http://learnersdictionary.com/3000-words http://learnersdictionary.com/3000-words [2] https://github.com/dwyl/english-words https://github.com/dwyl/english-words
- hvidgaard 10y ago
  There is not 3000 _core_ words. You don't teach elementary school children 3000 words. That list is significanly smaller. In Denmark it's 120 words, then you'll be well on your way to reading and writing most basic stuff. That someone has selected 2048 words used to generate passphrases, doesn't make it easy to remember.
  - rsanders 10y ago
    I've been doing this for years and it is indeed easier to remember. You won't be keeping all your passwords in your head in any format if you're using a unique password per site or service as you should. But you occasionally have to buffer them mentally between your password manager and the input box (especially on mobile), and the same number of bits of entropy are infinitely easier to copy correctly in this format vs something like "?G[G6n|4".
  - aangjie 10y ago
    Err.. I would suspect most(non-english?) people on the internet to know 2000 words. (By virtue of being atleast bi-lingual, they would, so the challenge boils down to can they type it? unicode support should help, but I've found most cases people simply type those sounds in English.) As for the English as a primary language people, I've no clue about the number of words, but if we can expect them to type 1024 words, we'd still get 20 bits..