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Disclaimer: I'm a beginner to cryptography.

Background: I'm reading Cryptography Engineering by Ferguson, Schneier, and Kohno, where the authors use this image:

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Question: What do the commas mean here?

My attempt: m, c := --- seems to mean "given" m, c equals ...

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It's a comma to separate the two things. Alice has $m$ and can calculate $c$ which is equal to $E(K_{e}, m)$. Bob has $c$ and can calculate $m$ which is equal to $D(K_{e}, c)$.

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Yes, exactly.

This can be read as "given m, c is defined as the encryption of m, with the key Ke"

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    $\begingroup$ Probably better to say 'defined as' instead of 'equals'. At least, for pedagogical purposes. $\endgroup$
    – Reid
    Feb 25, 2016 at 1:17
  • $\begingroup$ @Reid I'll agree, however, can you give me a rundown of the change in meaning from a pedagogical standpoint? $\endgroup$
    – d1str0
    Feb 25, 2016 at 2:42
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    $\begingroup$ Well, it's really from multiple perspectives... The first is just that the := symbol typically means "defined as", so it's good to use the same language as everyone else. The second is a little vaguer: In my experience teaching, a frequent source of student confusion is the difference between "derived"/"obtained" objects versus arbitrarily-named objects. Saying "c is defined as..." just highlights that we're calling this thing c, not that we did something special to arrive at a value for c. $\endgroup$
    – Reid
    Feb 25, 2016 at 4:16

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