Say I selected two large primes
q for RSA and computed my public key
(e, n=pq) and my private key
Now, I was careless and compromised my private key
q were not leaked. Taking into account that
(e, n) were already public knowledge, would it be safe to generate a new key pair with the same
q or are they somehow compromised by the leaking of the private key?
If it would not be safe, how could someone compute
q from my public-private key pair?