If you have a public address and you reuse this address to send BTC from multiple times, my understanding is that your public address is more susceptible to being hacked (ie. easier for somebody to generate the private key from your public address). From what I have read, if you send BTC from your public address and you keep any leftover coins in that public address, your public address is only protected by ECDSA. I have also read that the more you reuse the same address to send BTC, the more your address is susceptible to being hacked.
So let's say I am using a public address. I send a portion of my BTC from my public address to somebody else but the leftover BTC remains in my public address (doesn't Electrum keep your leftover BTC in the same address by default?). I use this same public address to send BTC from over the next several weeks. In total, I have sent from this address 4 or 5 times over several weeks. Several weeks later, after I am done sending my BTC, I backup my wallet and my private key, uninstall Electrum and decide to let my leftover BTC sit there in my public address.
With today's technology, how long would it take to hack this public address? Is this something I don't have to worry about for the next 10 years? The next 5 years? The next 1 year?
Let me run this question as an answer. Say you gen a private key and public address pair, then you keep generating addresses for a long time with that public-key.
What happens is that each address is just a I*PubKey ( where I is the i'th address you generated from that mother public-key ) that is hashed, so the more you use that same pubkey to generate addresses you increase probability that I will hit your address with my pub-key guess box, everytime you use the same public-key to gen an address its a dart on the wall, an the more darts on the wall the higher probability that I will hit that dart.
It's easy to guess private-keys, and its easy to make a public-key from them, and then its super easy to generate 10k addresses from that public-key and test them all in a second,
... Its not easy to take a public-key and make a private-address, but the more addresses you generate the easier it is for me to guess your private key.
For me I have all the addresses known on BTC on my wall, thus I'm not likely in all history of universe to hit your address, unless you have lots of them for me to 'sticky' on my wall.