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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). Bob should generate a new modulus, this is not that expensive. Also, Bob should revoke his old public key, if it is registered anywhere. |
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