Just to be clear, that's in addition to having the same message and private key, right?
reusal of address(privkey) and the random parameter k can cause trouble
Can you explain this more?
What kind of trouble?
Reusing the same nonce value (hence same k value) on two different signatures (ie. different messages) signed with the same private key, leaks the private key. This has happened in Bitcoin due to bad nonce generation code, and quite a few times, and has led to loss of funds.
The wikipedia page on ECDSA explains the algebra; it's a very simple calculation to do.