I'm trying to clear up my confusion in using the term "discrete" in discrete logarithm. I'm focusing on why the word "discrete" is used to differentiate it from a logarithm.
Wikipedia defines a discrete logarithm as follows:
in any group $G$, powers $b^k$ can be defined for all integers $k$,
and the discrete logarithm $log_b a$ is an integer $k$ such that $b^k
= a$.
Is the term discrete added simply to reflect the fact that $k$ in $log_ba=k$ is confined to integers? Or is it a combination of the discrete log being an integer as well as the powers fulfilling the properties of a group $G$?
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