In the RSA context, why is not safe to use the same n (public key)for different people?

  • Do you mean sharing a private key amongst multiple people?
    – atk
    Oct 29, 2014 at 0:16
  • not the private key, the public key with multiple people
    – JuanMan394
    Oct 29, 2014 at 0:30
  • But what use is multiple people having a single public key, if not (a) also sharing the private key, or (b) using it in the normal way to encrypt messages to the holder of the associated private key? The question sounds like either a trick question intended to imply the former or a total misunderstanding of how the latter works...
    – atk
    Oct 29, 2014 at 0:34
  • I don´t understand the question too, I was studying RSA, I was specially to asked explain the algorithm in the page 8th of this document cs.purdue.edu/homes/ninghui/courses/Fall04/lectures/… , and then my teacher asked me to explain (based on that document) why is not safe to use the same N for multiple people
    – JuanMan394
    Oct 29, 2014 at 0:44

1 Answer 1


The modulus is usually bound to the key pair. If somebody would want to sign or decrypt anything he/she would basically have to use the same private key. Obviously you cannot generate a valid private key if you only have knowledge about the public key, that would defeat RSA.

If you want a more theoretical answer, then I wish you luck and a good mathematical background.


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