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Suppose I have two messages $m_1$ and $m_2$ as well as $c_1$ and $n$. It's standard RSA so $c_1 = m_1^e \ mod \ n$, $c_2 = m_2^e \ mod \ n$. Further assume the only information we have about e is that it is smaller than $2^{2048}$. Is there a way to find it? (According to this it is not)

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  • $\begingroup$ Is there some reason why you think the answers to that duplicate you linked to would be wrong? $\endgroup$ – Ilmari Karonen Apr 22 at 21:11
  • $\begingroup$ no particular one, I just couldn't wrap my head around it for some reason. $\endgroup$ – S. L. Apr 23 at 9:34
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No, it is not possible.

If it were, then RSA would be insecure; the same way to recover $e$ from $m_1, m_1^e \bmod n$ would be able to recover the private key $d$ from $c_1, c_1^d \bmod n$ (as that's the same problem, only using different symbols).

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  • $\begingroup$ :facepalm: of course. $\endgroup$ – S. L. Apr 22 at 19:25

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