Replace MathJax with MathML (#2477)

Signed-off-by: Daniel Gray <dngray@privacyguides.org>
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Jonah Aragon 2024-04-03 12:40:26 +00:00 committed by Daniel Gray
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@ -82,11 +82,62 @@ We recommend using [EFF's large wordlist](https://eff.org/files/2016/07/18/eff_l
To demonstrate how strong diceware passphrases are, we'll use the aforementioned seven word passphrase (`viewable fastness reluctant squishy seventeen shown pencil`) and [EFF's large wordlist](https://eff.org/files/2016/07/18/eff_large_wordlist.txt) as an example.
One metric to determine the strength of a diceware passphrase is how much entropy it has. The entropy per word in a diceware passphrase is calculated as $\text{log}_2(\text{WordsInList})$ and the overall entropy of the passphrase is calculated as $\text{log}_2(\text{WordsInList}^\text{WordsInPhrase})$.
One metric to determine the strength of a diceware passphrase is how much entropy it has. The entropy per word in a diceware passphrase is calculated as <math>
<mrow>
<msub>
<mtext>log</mtext>
<mn>2</mn>
</msub>
<mo form="prefix" stretchy="false">(</mo>
<mtext>WordsInList</mtext>
<mo form="postfix" stretchy="false">)</mo>
</mrow>
</math> and the overall entropy of the passphrase is calculated as: <math>
<mrow>
<msub>
<mtext>log</mtext>
<mn>2</mn>
</msub>
<mo form="prefix" stretchy="false">(</mo>
<msup>
<mtext>WordsInList</mtext>
<mtext>WordsInPhrase</mtext>
</msup>
<mo form="postfix" stretchy="false">)</mo>
</mrow>
</math>
Therefore, each word in the aforementioned list results in ~12.9 bits of entropy ($\text{log}_2(7776)$), and a seven word passphrase derived from it has ~90.47 bits of entropy ($\text{log}_2(7776^7)$).
Therefore, each word in the aforementioned list results in ~12.9 bits of entropy (<math>
<mrow>
<msub>
<mtext>log</mtext>
<mn>2</mn>
</msub>
<mo form="prefix" stretchy="false">(</mo>
<mn>7776</mn>
<mo form="postfix" stretchy="false">)</mo>
</mrow>
</math>), and a seven word passphrase derived from it has ~90.47 bits of entropy (<math>
<mrow>
<msub>
<mtext>log</mtext>
<mn>2</mn>
</msub>
<mo form="prefix" stretchy="false">(</mo>
<msup>
<mn>7776</mn>
<mn>7</mn>
</msup>
<mo form="postfix" stretchy="false">)</mo>
</mrow>
</math>).
The [EFF's large wordlist](https://eff.org/files/2016/07/18/eff_large_wordlist.txt) contains 7776 unique words. To calculate the amount of possible passphrases, all we have to do is $\text{WordsInList}^\text{WordsInPhrase}$, or in our case, $7776^7$.
The [EFF's large wordlist](https://eff.org/files/2016/07/18/eff_large_wordlist.txt) contains 7776 unique words. To calculate the amount of possible passphrases, all we have to do is <math>
<msup>
<mtext>WordsInList</mtext>
<mtext>WordsInPhrase</mtext>
</msup>
</math>, or in our case, <math><msup><mn>7776</mn><mn>7</mn></msup></math>.
Let's put all of this in perspective: A seven word passphrase using [EFF's large wordlist](https://eff.org/files/2016/07/18/eff_large_wordlist.txt) is one of ~1,719,070,799,748,422,500,000,000,000 possible passphrases.