Quote from: pand70 on December 16, 2013, 09:44:51 AM

Quote from: CoinGeneral on December 16, 2013, 04:06:56 AM

Actually - given enough time - is it theoretically possible to crack the private key to that address?

I mean in the future computers will be 1000x more powerful than they are today.

Will our brains be blown out of our bodies?

This is something that is addressed many times before. While the obvious answer is yes there are some physical limitations that don't allow something like it to happen. In quantum physics though seems possible.

Exactly. As the quote in the "star image" was mine, I want to avoid it being taken out of context. As you point out if you can't go through the wall there may be other ways around it. The quote only deals with brute forcing a 256 bit key (and subsequently to writing that quote I have learned that a 256 bit ECDSA key only has 128 bit strength against brute force attack although that doesn't materially change the scenario in the quote). It only deals with a brute force attack and I wrote it because I got tired of all the "what if computers get faster can someone hack Bitcoin questions". Still it is important to keep in mind that there are other attack vectors which don't deal with a classical brute force (and the physics problems that accompany it).

If you wanted to gain access to coins at a random Bitcoin address there are three attack vectors:

Brute force attack on all the private keys used in the Bitcoin network = infeasible given the time and energy requirements (the "star quote").
Exploit a cryptographic flaw in ECDSA, RIPEMD-160, and/or SHA-256 = no such known flaw exists at this time and may not exist in our lifetime.
Use a general Purpose quantum computer capable of implementing Shor's algorithm = may not ever be possible or if possible the time until a GPQC with 40,000+ qubits is indeterminable.

All three are infeasible right now, only the first one is beyond the limits of physics the other two simply don't exist right now. Maybe they will exist next year, maybe not for a thousand years but we do know that they are possible on a long enough timeline. The good news is that Bitcoin is extensible and long before either cryptoanalysis or quantum computing make an attack economical or practical Bitcoin can be extended to new stronger address types including ones which are quantum computing resistant. People can transfer funds to the new addresses and avoid the attack vector (for another century or so). Of course funds for which there is no known private key ("lost coins") could at least in theory be reclaimed because they won't be moved to the stronger address scheme but it won't be as some incorrectly believe "because computers get faster".