# RSA : Is there a way to compute phi(n) or N itself if we only know e, d and a ciphertext?

I am trying to solve a problem where private key exponent d, ciphertext c, and public key exponent e (65537) are known. How can I calculate φ(n) or n itself?

An extended version of the problem would be : If we can get many d and ciphers for the same plaintext, where e is always 65537, is there a way to decrypt the cipher?

• Couple of hints - what is the definition of $e$ and $d$? How do they relate to $\phi(N)$? Mar 16 at 18:31
• Hints given are more than enough to solve this without number theory. Mar 16 at 19:10
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– fgrieu
Mar 17 at 11:54