The phrase buck naked is well known and means "completely naked". It is synonymous to butt naked and stark naked, both self-explanatory. However, there are a few confusing aspects to the etymology of buck naked.
My research brought me across a few plausible explanations:
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The word "buck" comes from buckskin, which is a deer/horse like animal.
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A slang used by Americans against natives(Indians) for young males who often fought or hunted without clothing.
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It is a Bowdlerization of "butt naked" so that it can be used in public without causing unnecessary discomfort. A euphemism of some sort.
All three explanations seemed equally possible to me and I failed to unearth an authoritative source to confirm any of them.
It would also be interesting to know if the phrase is more popular in some parts of the world than others.
Best Answer
The possibility you left out is that, rather than a bowdlerisation of "butt naked," it was an eggcorn of it; however, determining whether such a change was deliberate or accidental would be nigh on impossible.
Of the three, we can argue in favour of the second, though with the people referenced being as much those of African as of American origin.
We find "buck naked" in the 19th Century.
We do not find "butt naked" during that period.
We do not find it any earlier.
We do find "buck" being used to refer to men of African and of American Indian origin.
We do find the lack of clothing in some parts of Africa and America remarked upon. We also find slaves in the American South often working with little clothing. (We also find it overstated, a cartoon of an African might likely feature them as naked even if that would be highly unlikely in the scenario depicted — we're talking about people with some pretty strong racial prejudices here).
As such, we have a group of people being called "bucks" whose nakedness is often remarked upon. This suggests that the likelihood of it being the origin is quite high.
It's far from conclusive though, and you aren't going to get any better unless you hit documents from the period and manage to track it down better yourself.