# Is sharing the modulus for multiple RSA key pairs secure?

In the public-key system RSA scheme, each user holds beyond a public modulus $m$ a public exponent, $e$, and a private exponent, $d$.

Suppose that Bob gives his private exponent to other users. Rather than generating a new modulus, Bob decides to generate just a new public and a new private exponent $e'$ and $d'$.

Is this safe for Bob?

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No, it isn't safe. Knowing the private exponent $d$ (and a corresponding public key) allows factoring the modulus $m$, and this allows retrieving all other private exponents (given the public ones).