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I have two different ciphertexts $c_1$ and $c_2$, and two different public keys that share the same modulus such that $e_1 \neq e_2$ but $n_1 = n_2$.

  • What attack can I use to recover the private keys?
  • Common modulus attack works only if $c_1 = c_2$, doesn't it?
kelalaka
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    This might be a homework question. – kelalaka Oct 22 '19 at 19:36
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    Obviously the question is about textbook RSA. Also, something must be known about the plaintext(s); such that: they are the same. Otherwise, $c_1$ and $c_2$ give no information and the only way is factoring $n_1$. – fgrieu Oct 22 '19 at 19:41
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    Actually, even with textbook RSA, there isn't a way to recover the private key, even if the messages were the same. You could recover the common message (assuming $e_1, e_2$ are relatively prime), and that's a standard textbook attack... – poncho Oct 22 '19 at 21:55

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