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When talking symmetric encryption, a 56 bit key is known to be so weak. If you use it for your encryption, you are considered a goner.

When talking passwords however, the standard these days is about 8 characters selected from about 94 characters on the keyboard. This translates to about $94^8$ possible passwords, which means about 52 bits of entropy.

Now, 52 bits is obviously less than 56 bits. But somehow a 56 bit key is considered weak while a 52 bit password is considered safe (i.e., many systems force you to use the 8 characters). Why is this so; I mean why are the standards lower when we talk passwords yet both passwords and keys are subject to the same kinds of brute-force attacks?

I know that humans would find it impossible to maintain a 128 bit password -- however, I wonder if there is some technical reason why a 52 bit password would not be as weak as a 52-bit encryption key for that matter.

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    $\begingroup$ Personally I use a password with 130 bits of entropy. And I have noticed how even people who people who usually wouldn't be considered very intellectual are still able to memorize facts which have way more than 130 bits of entropy. So the apparent inability to memorize strong passwords from what I have seen seem to be more tied to willingness to spend time memorizing and how it is presented, rather than not being able to retain 130 bits of entropy. $\endgroup$ – kasperd Jun 5 '16 at 11:12
  • $\begingroup$ passwords used online can't be guessed a million times a second like a captured ciphertext can. $\endgroup$ – dandavis Jun 7 '16 at 7:53
  • $\begingroup$ "This translates to about 94^8 possible passwords, which means about 52 bits of entropy." hmm.. How did you calculate this? $\endgroup$ – Aydin K. Jun 7 '16 at 17:29
  • $\begingroup$ If each of these passwords is considered to be equally likely, the entropy formulation should boil down to log2(N) where N is the number of possibilities. Could I be wrong? I stand to be corrected. $\endgroup$ – Minaj Jun 7 '16 at 17:45
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    $\begingroup$ @Aydin: If EACH symbol in an 8-symbol password had an equal likelihood of being selected from a pool of 94 total symbols, then the entropy of each symbol in the set would be 6.5545 bits, and the resultant entropy of the password would be 52.4367 bits. But, people don't create random passwords very well at all, so Shannon determined that symbol entropy is actually closer to 1.3 bits each--nowhere near 6.5. So a "human" password of complexity 94^8 would really have an entropy of about 10.4 bits--nowhere near 52. The takeaway: entropy trumps complexity. $\endgroup$ – Mac Mar 15 '17 at 14:37
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I know that humans would find it impossible to maintain a 128 bit password -- however, I wonder if there is some technical reason why a 52 bit password would not be as weak as a 52-bit encryption key for that matter.

First, I would argue that 128 bits is not impossible to remember. My current password manager master password is almost 100 bits (6 words from a large dictionary) and I could increase it to 128 bits if I wanted to by tacking a couple of extra words at the end.

However, yes, there are reasons passwords with much less entropy are often considered acceptable:

  1. It is good practice to use a good password hash that slows down attacks to a similar degree as e.g. an extra 20 bits of entropy would.
  2. Many uses of passwords do not allow an offline attack with as much computing power as the attacker has. E.g. a login password on a website can only be attacked online, usually with a strict rate limit. (Until the password hashes are stolen.)
  3. Two-factor authentication is seeing some use. With it finding the password alone is insufficient.

When some of the above factors do not apply you need to make sure you have enough entropy. E.g. a "brainwallet" Bitcoin password does not benefit from 2. or 3. so it should have at least the 50+ bits so that a password hash makes attacking it too expensive to be worth the effort.

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  1. I seriously doubt the standard for passwords these days being 8 characters. I would consider anything below 10 characters seriously flawed. I personally always use 20 character passwords.

  2. Often, encryption keys are used as such, while passwords are (or at least should be) strengthened with a KDF. The vulnerability of an n bits password or key depends on the attack speed, and a heavy KDF (such as scrypt) significantly decreases the attempts per second that can be done to brute force the password.

  3. Rare exceptions excluded, humans are not supposed to remember (or create) passwords in the first place. There's software for that which does a much better job.

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