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

sz flag

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?

Kolja avatar
cn flag
Couple of hints - what is the definition of $e$ and $d$? How do they relate to $\phi(N)$?
kodlu avatar
sa flag
Hints given are more than enough to solve this *without* number theory.
fgrieu avatar
ng flag
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