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Defining entropy in “layman’s terms”

My response to a post on security.stackexchange.com

 

The layman’s part comes later, but first, let’s get scientific.

I struggled to understand the concept of mathematical entropy, but, lucky for me, I work with a physicist. When I asked him to explain it, he directed me towards the graphs of two laws: uniform distribution and normal distribution.

Knowing the Y-axis describes a measurement of probability of guessing the password, and X-axis describes a value of what the password is… in a uniform distribution (see diagram), the entropy is high, because no matter what the password is, the probability of guessing it is the same value (high). In a normal distribution (see diagram), the probability of guessing the password changes… for instance, you’re ~70% likely to be able to guess the password (sort of).

For the layman…. Where’s Waldo/Wally?

High entropy:

  • You’re trying to find Waldo by identifying what he’s wearing.
  • You are given 100 people.
  • 100 of these people are dressed like Waldo, including Waldo.
  • Where is Waldo?

∴ You have a very little chance of identifying Waldo.

Low entropy:

  • You’re trying to find Waldo by identifying what he’s wearing.
  • You are given 100 people.
  • 33 of these people are dressed like Mark, 33 are dressed like John, 33 are are dressed like Tom, and 1 is dressed like Waldo (and is Waldo).
  • Where is Waldo?

∴ You have a very high chance of identifying Waldo.

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