On Jul 13, 2018, at 2:22 PM, David Mason <dma...@ryerson.ca> wrote:
>
> Acgq75VpCWjdsJaa5abe9JeX3I (don't worry, this isn't a real password to
> anything)
>
> …I fed this through an online entropy calculator and got 4.29 bits of Shannon
> entropy
That calculator is giving you bits *per character*.
You can see this several ways:
1. Double the message and the bits per character doesn’t change because the
size of the source alphabet doesn’t change.
2. Add a dollar sign to the message, and bpc goes up a bit. (This conflicts
with your report that adding a special character didn’t change it, but it did
for me.)
3. Turn on the calculator’s case folding option and the bpc value goes down a
bit.
One key realization you should get from this calculator is that ASCII text is
not 7 or 8 bits of entropy per character. It simply is not, because not all
characters in the source text are equally likely. Many code points may never
be used in a given corpus.
Another realization is that a random blob of hex noise should asymptotically
approach 4 bpc, since each character is 4 bits of data, and the data are
supposed to be evenly distributed across the code space.
Here’s some noise from grc.com/pass:
C79683189EFBEBEC30A4C1A6D733F0242FB48E2582F3B2E7581D85E91E0A2FA5
The initial value is 3.91, and pasting it in a bunch of times does increase the
value towards 4, suggesting it’s got pretty good entropy.
Now paste in an equivalent number of ‘a’ characters, and you get 0 bits of
entropy. Strictly speaking, you get 1 bit of entropy for the whole message,
but it shows 0 because the calculator is rounding the result off to 3
significant figures.
> So I tried:
> dd if=/dev/random bs=100 count=1|od -c
> and the result only gave 5.00 bits
That’s plausible. With a much larger sample, the result should approach 7, 8,
16, or 21, depending on your local character set size. (Respectively: pure
ASCII, ISO 8859 or similar, UCS-2 and full Unicode.)
Now see if you can guess the asymptotic ideal for this slightly different
command:
$ dd if=/dev/random bs=100 count=1 | od
Spoiler below.
………..
3, because the output is restricted to octal, thus 3 bpc.
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