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Kind of an old question, but I just figured this out myself, so just in case you don't have the answer, here goes...

For the inline equation, I was able to compile using

latexmath:[$(mathbb{F}_p)$]

The second one, you don't need to use begin{equation}. AsciiDoc takes care of that for you. Instead just do

[latexmath]
+++++++++++++
{K = k * G}
+++++++++++++

That's if you actually want the curly braces. See here for more details.

Also, if you want to use the equation environment to have your equation numbered, you can use [latex] instead of [latexmath].

[latex]
----------------------------------
begin{equation}
.
.
.
end{equation}
----------------------------------


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