Why would you need 10 signatures or more? According to mathematics, if there were a way to find or derive the private key with 2, it would be sufficient, because the path would be to derive the nonce, and once this is done, you obtain the private key. As far as I know, this is only possible if you use the same nonce in 2 signatures or when it is insecure. Why 200 bits, what is special about this? 200 bits are still secure today.

I recommend inserting code correctly with :