Suppose that you have an encrypted message and a decrypted message (just one). M (the public key) and k (the exponent you raise each number to) are public. Does having one copy both version of a message give you enough information to decrypt other messages? I think the question boils down to finding the value of the euler phi of M which is not easy if you don't know its factorisation. I don't think there is a way to decrypt other messages but I'm not sure and am thankful for any help in advance.

  • $\begingroup$ The NSA will be knocking at your door shortly... $\endgroup$ – user137500 Mar 24 '14 at 3:09
  • $\begingroup$ @user137500 The NSA doesn't need to knock at your door, it already knows all that it needs to! :P $\endgroup$ – qwr Mar 24 '14 at 3:11
  • $\begingroup$ Have you seen my answer? Any questions about it? $\endgroup$ – Gerry Myerson Apr 6 '14 at 10:50

Take any message you like. Encrypt it. You now have in your possession both an encrypted message, and the decrypted message. Does that help you to decrypt other messages?

  • $\begingroup$ Yup that's what I came up with. $\endgroup$ – user137538 Apr 7 '14 at 12:14

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