I'm studying the RSA protocol and I was wondering if there was any way of decrypting a message if the $e$ doesn't have an inverse $\mod (p-1)(q-1)$.

Usually, you have to choose a value of $e$ that is inverse $\mod (p-1)(q-1)$, but I made a mistake in my calculations. If someone where to write to me using the formula $C = M^e \bmod n$, would there be any way for me to decrypt it if my $e$ is wrong or am I out of luck.

  • $\begingroup$ What is the value of $e$? Is this textbook RSA? This seems like homework! $\endgroup$ – kelalaka Nov 12 '19 at 22:56
  • $\begingroup$ It's one of my friend who messed up his assignment and I'm trying to find a way to help him out. He sent a randomized $e$ instead of one that has an inverse with $(p-1)(q-1)$ the assignment is to open an excel file which the teacher sent us encrypted using our $e$. I don't think the $e$ alone can help you. I don't have it with me right now but I can send it later if you think it could help. $\endgroup$ – Manuel Ramirez Nov 12 '19 at 23:06
  • $\begingroup$ This means that $\gcd(e,\varphi(n) = d \neq 1$, you might get some information by working on $e/d$ and $n/d$, however, I'm not sure that the xml can fit one RSA encryption. $\endgroup$ – kelalaka Nov 13 '19 at 2:17

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