- snip -
but it is possible.
- snip -
No it isn't.
Perhaps you are using a VERY different definition of the word "possible" than most of the world uses.
- snip -
a quantum computer, how would that have an impact?
If the protocol wasn't changed at all, then once someone spent some bitcoins which were received at an address (which results in the public key being broadcast) it might become possible to compute the private key. This isn't a certainty, and the first available quantum computers won't be very good at it, but given enough time quantum computers might be developed that could.
There are a few things to keep in mind here:
1. "Quantum" doesn't mean "magic" or "super-duper fast". Quantum computing is a completely different way of handling calculations. It is very good at some types of calculations, and very bad at other types.
2. Much like the computers of the 1940's and early 1950's, the first quantum computers aren't going to be able to do a lot. Over years (probably decades) they may be improved upon and get more versatile, but initially they'll be limited in their usefulness.
3. There will be time to modify the bitcoin transaction types to be even more resistant to the abilities of quantum computers.
4. Bitcoin addresses are already quantum resistant. The public key is not initially given out. It is passed through the SHA256 hashing algorithm and then the result of that through the RIPEMD160 hashing algorithm. It is only result of the RIPEMD160 hashing algorithm that is intially stored in the blockchain when you receive a transaction. Since quantum computers aren't very good at reversing hashing algorithms, this protects the bitcoins your receive. It is only when you spend those bitcoins that the public key becomes publicly known. So, if you never re-use a bitcoin address (always generate a new address for every transaction that you receive), then none of your bitcoins will ever be sitting at an address with a publicly known public key.
Let's say someone has one and set it's task to generating addresses, would such a person be able to drastically 'improve' his changes to 'find' addresses which are already taken/have some Bitcoins in them, i.e. address collision?
No.
Brute forcing a bitcoin address will still be impossible. It can be difficult for humans to grasp just how bit the numbers are that we are dealing with. It's a bit like saying: "I know that dumping this teaspoon of fresh water into the ocean isn't going to noticeably change the salinity of the ocean, but what if I dump this 5 gallon bucket in? Would that reduce the ocean's salinity in a significant way?