Say I selected two large primes p
and q
for RSA and computed my public key (e, n=pq)
and my private key (d)
.
Now, I was careless and compromised my private key (d)
. p
and 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 p
and q
or are they somehow compromised by the leaking of the private key?
If it would not be safe, how could someone compute p
and q
from my public-private key pair?