There are issues when you create a signature in ECDSA - it requires a random number, k & a hash of the transaction. The algorithm computes a number r from k, and computes the signature s, and returns (r, s). If you have two signatures, from the same private key, and the same r (aka, k), you can use algebra to solve for the private key.
This can be avoided by using deterministic k values in signatures though, so that they never sign with the same k.
The first is your least concern anyway! The second shouldn't be a problem, but the android wallet vulnerability has shown people need to draw from high entropy randomness, otherwise the keys just aren't strong enough. Someone else may eventually find one. I quite like the deterministic scheme, it goes a good job of preventing the second.
Thanks for the informative reply. So address reuse cannot expose the random number generator scheme of the machine. It is a problem when k is reused but a sequence of k's generated cannot give any info about the random generation algorithm so other private keys generated by the machine are safe.
Also multiple time signing with different k's does not weaken ECDSA right? For example reducing the search space.
Is the 1st or 2nd a problem for sigsafe? Isnt it using just 1 address?