Given N and e in RSA and the ability to get signature s for any message m ($s=m^d \mod{n}$), can you find the value of the private key d?

  • $\begingroup$ Did you search on our site? Are you asking for a TextBook signature that is already insecure? Or are you asking for RSA-PSS? Note that signature requires hashing of the message since the first true Rabin Signature Scheme, $\endgroup$
    – kelalaka
    May 25, 2021 at 14:10
  • $\begingroup$ @kelalaka on the site I found this crypto.stackexchange.com/questions/9896/… that shows how to find a signature m without d and I also found how to find N without having it initially, but I haven't found how to work out d given N and e and the ability to find the signature for any message m. The signature I'm talking about is $s=m^d\mod{n}$ and you can modify m to any value you like and receive the value of $s$ $\endgroup$ May 25, 2021 at 14:12
  • $\begingroup$ Nope, signature requires the private key. $\endgroup$
    – kelalaka
    May 25, 2021 at 14:38
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    $\begingroup$ Hint: If you can find, then you can solve factorisation problem, too $\endgroup$
    – kelalaka
    May 25, 2021 at 14:44
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    $\begingroup$ @JamesTheAwesomeDude those are about encryption, the question is about the signature. $\endgroup$
    – kelalaka
    May 25, 2021 at 17:11


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