I understand in theory how the common modulus attack works (as described here: how to use common modulus attack?) Though, I did not understand completely how it worked with a negative $s_i$. Since ...
Are RSA or ECC vulnerable to an attack where the same (unknown) plaintext is encrypted with multiple public keys?
I'm not sure what this attack model is called - it's not known-plaintext and also not quite cipher-text-only. It is similar to this question except the general case (not just two keys) and using keys ...
Suppose your private key $d_1$ has been exposed. Instead of changing $p$ and $q$, instead you just choose a new public and private key (say $e_2$ and $d_2$) and use these instead. What kinds of ...