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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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  • $\begingroup$ Related questions (but which do not directly address my question) crypto.stackexchange.com/questions/53232/…, crypto.stackexchange.com/questions/34041/…, crypto.stackexchange.com/questions/76089/… $\endgroup$
    – eddydee123
    Commented Dec 30, 2021 at 18:59
  • $\begingroup$ @kelalaka IIUC the answer there is it's mathematically imprecise, but it is indeed nit-picking $\endgroup$
    – eddydee123
    Commented Dec 30, 2021 at 19:03
  • $\begingroup$ @kelalaka So shall I delete my question? $\endgroup$
    – eddydee123
    Commented Dec 30, 2021 at 19:31
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    $\begingroup$ No need, it has already been closed; having a dupe may lead other persons looking for the same Q/A to the right answer. $\endgroup$
    – Maarten Bodewes ♦
    Commented Dec 30, 2021 at 20:42
  • $\begingroup$ @MaartenBodewes yes, you are right, however, I did not like the title change of the dupe! $\endgroup$
    – kelalaka
    Commented Dec 30, 2021 at 23:33

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