firstly What do you mean about security? everything is cleared in Satoshi book .
About security, only then yours BTC are safe where/when:
1. Your public addres has no output transactions
2. If your public address has no more output transactions than 4.

you ask me why step 2?

for example: if and only if you have more transactions output that n , example : 40 (as  outputs -  40 x r,s,z)

you can try implement algorithm - superpositional linear equation -  and you need to find only 4 transactions in the same level bit  to recalculate private key.

everything is "depends on"

bitcoin or secp256k1 -> we can't tell about security, or we can't tell about "break", because there is nothing to break,
if you know what are you do, you can "do everything"