5 ms·

I don't understand how 4 random words from a 50k dictionary gives 90 bits of entropy. 50k ^ 4 => 6.25e+18 2 ^ 90 => 1.24e+27 Am I missing something?

saurik 12y ago
The words are separated (and I guess terminated) by a random symbol (of which there are apparently 32 possibilities) or (randomly) a random two-digit number. log(50000^4*(100+32)^4)/log(2) = 90.6
- ghshephard 12y ago
  Doesn't that defeat the "Trivial to remember" part of the xkcd concept of "Trivial to remember, hard to guess?"
  - mtct 12y ago
    https://www.schneier.com/blog/archives/2014/03/choosing_secure_1.html https://www.schneier.com/blog/archives/2014/03/choosing_secu...
  - stcredzero 12y ago
    That means you only have 7 entities to remember, which is supposed to be what humans can handle easily. (Though I understand now that this is stale knowledge.)
    - aggie 12y ago
      The number refers to the capacity of working memory and has indeed been revised over time. It's a complicated issue, but 4 units of information is now considered a more accurate approximation. But if you're remembering a password, you're dealing with long-term memory, which doesn't have this limitation. http://en.wikipedia.org/wiki/Working_memory#Capacity http://en.wikipedia.org/wiki/Working_memory#Capacity
      - miga 12y ago
        Long-term memory usually accepts most information from short-term memory not direct sensory input, so it is easier to memorize when you break down things in chunks first.
atmosx 12y ago
Can you offer a link on how do you do these measurements and what exactly do they mean? Reading the wikipedia article about entropy in (computing) I stumbled across this[1]: " Around 2011, two of the random devices were dropped and linked into a single source as it could produce hundreds of megabytes per second of high quality random data on an average system. " What does it mean high quality random data in this context?. I mean 'random' is a precise definition, something 'is random' (e.g. distance of next prime :-P, kill Riemann) or 'not random' (distance of next prime if Riemann's ζ(s) is solved). [1] https://news.ycombinator.com/user?id=dasil003 https://news.ycombinator.com/user?id=dasil003
- tinco 12y ago
  That's random in maths, we're not talking maths here. In the real world, random is a value that's hard to predict. For example a dice throw has a high quality of random in normal circumstances. A low quality random source would depend on some variables that make it easier to predict the next random number (perhaps just statistically). The worst quality random source would be pseudo-random numbers, where the value of each next random number directly follows from the previous value and perhaps some secret second value. It might be distributed like a true random number, but eventually the secret could be guessed and the numbers would become predictable.
- darkmighty 12y ago
  A simple explanation is that "randomness" here is related to (logarithm of) the minimum average time [1] you would take to guess the password correctly (H=sum(pi * log(1/pi)). Since the random number generator supposedly gives an uniform distribution over a set of words, this simplifies to H=n(1/n log(n))=log(n). [1] Your average time is at least t* =1/2 * 2^H, so log( t* )>H-1.
- ef4 12y ago
  "Distance of next prime" is not random, it's entirely deterministic. It's a well-defined function. Just because we don't have an analytical solution for it doesn't make it random. As for "high quality", some random variables are less predictable than others. A weighted coin that comes up heads 51% of the time is still random (not deterministic), but more predictable than a fair coin.
deleted 12y ago
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Ruud-v-A 12y ago
I wrote a post about this some time ago: http://ruudvanasseldonk.com/2012/07/07/passphrase-entropy http://ruudvanasseldonk.com/2012/07/07/passphrase-entropy

saurik 12y ago

The words are separated (and I guess terminated) by a random symbol (of which there are apparently 32 possibilities) or (randomly) a random two-digit number. log(50000^4*(100+32)^4)/log(2) = 90.6

ghshephard 12y ago
Doesn't that defeat the "Trivial to remember" part of the xkcd concept of "Trivial to remember, hard to guess?"
- mtct 12y ago
  https://www.schneier.com/blog/archives/2014/03/choosing_secure_1.html https://www.schneier.com/blog/archives/2014/03/choosing_secu...
- stcredzero 12y ago
  That means you only have 7 entities to remember, which is supposed to be what humans can handle easily. (Though I understand now that this is stale knowledge.)
  - aggie 12y ago
    The number refers to the capacity of working memory and has indeed been revised over time. It's a complicated issue, but 4 units of information is now considered a more accurate approximation. But if you're remembering a password, you're dealing with long-term memory, which doesn't have this limitation. http://en.wikipedia.org/wiki/Working_memory#Capacity http://en.wikipedia.org/wiki/Working_memory#Capacity
    - miga 12y ago
      Long-term memory usually accepts most information from short-term memory not direct sensory input, so it is easier to memorize when you break down things in chunks first.

atmosx 12y ago

Can you offer a link on how do you do these measurements and what exactly do they mean? Reading the wikipedia article about entropy in (computing) I stumbled across this[1]: " Around 2011, two of the random devices were dropped and linked into a single source as it could produce hundreds of megabytes per second of high quality random data on an average system. " What does it mean high quality random data in this context?. I mean 'random' is a precise definition, something 'is random' (e.g. distance of next prime :-P, kill Riemann) or 'not random' (distance of next prime if Riemann's ζ(s) is solved). [1] https://news.ycombinator.com/user?id=dasil003 https://news.ycombinator.com/user?id=dasil003

tinco 12y ago
That's random in maths, we're not talking maths here. In the real world, random is a value that's hard to predict. For example a dice throw has a high quality of random in normal circumstances. A low quality random source would depend on some variables that make it easier to predict the next random number (perhaps just statistically). The worst quality random source would be pseudo-random numbers, where the value of each next random number directly follows from the previous value and perhaps some secret second value. It might be distributed like a true random number, but eventually the secret could be guessed and the numbers would become predictable.
darkmighty 12y ago
A simple explanation is that "randomness" here is related to (logarithm of) the minimum average time [1] you would take to guess the password correctly (H=sum(pi * log(1/pi)). Since the random number generator supposedly gives an uniform distribution over a set of words, this simplifies to H=n(1/n log(n))=log(n). [1] Your average time is at least t* =1/2 * 2^H, so log( t* )>H-1.
ef4 12y ago
"Distance of next prime" is not random, it's entirely deterministic. It's a well-defined function. Just because we don't have an analytical solution for it doesn't make it random. As for "high quality", some random variables are less predictable than others. A weighted coin that comes up heads 51% of the time is still random (not deterministic), but more predictable than a fair coin.

deleted 12y ago

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Ruud-v-A 12y ago

I wrote a post about this some time ago: http://ruudvanasseldonk.com/2012/07/07/passphrase-entropy http://ruudvanasseldonk.com/2012/07/07/passphrase-entropy