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This may be nit-picking, I’m not sure so feel free to say so.

In RSA-KEM as described e.g. in Wikipedia or this answer, we choose a secret $x : 0 \leq x < n$, and send $x^e \bmod n$ for public exponent $e$.

But isn’t this “textbook RSA”? For example, if $x^e \bmod n < n$ then it won’t wrap, and $x$ can be obtained directly.

Now of course for any normal $n$, the chances of choosing a random $x$ meeting this condition are infinitesmally small. Nevertheless isn’t it technically precise to choose $x: x < n$, $x^e \bmod n > n$ ?

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