How secure is the future?

[Tesla71]

I was wondering with the momentary increase in calculation power (asic's) wouldnt it be possible in the future to guess private keys out of the public keys in the blockchain?
So that one could look for an adress wich possibly has an high amount of coins and try to brute-force a wallet with that coins "in" it?

Think someone could tell me why that is impossible..

[btchip]

I'd not say impossible, but given the current attacks and key sizes, ECC 256 signatures are considered safe for the next 20 years.

Now let's assume there's a sudden mathematical breakthrough that allows people to reverse ECDSA, RSA, and other friends based on modular arithmetic - first, you'll have bigger issues to solve (banking cards and biometric passports use similar algorithms ), moreover bitcoin is a more difficult target as you could likely issue new keys faster than the attacker can break them.

[BlackBison]

Mining has nothing to do with the private key encryption, they use a different algorithm. Even if another ASIC was designed that could be used to brute force private keys it would only give say 1000x the efficiency max. Which is basically meaningless as the keyspace numbers are so astronomical we are talking a reduction down to billions of years instead of trillions of years.

The only danger is a flaw in ECDSA etc which has been pointed out.

[Tesla71]

OK, understand.
Another thing that bothers me is what would happen if some countries are disconnected from the internet or the connections between europe and usa will be down for some hours?
what would happen to the transactions and mined blocks on both sides if the connection is reestablished?
As far as I understood, because there is no centralization, the network would continue to function like normal (in case of enough hashing power on the "disconnected" site)?

[DannyHamilton]

OK, understand.
Another thing that bothers me is what would happen if some countries are disconnected from the internet or the connections between europe and usa will be down for some hours?
what would happen to the transactions and mined blocks on both sides if the connection is reestablished?
As far as I understood, because there is no centralization, the network would continue to function like normal (in case of enough hashing power on the "disconnected" site)?

If a geographical area becomes isolated, they will begin mining their own blocks separate from the rest of the world.  The world won't know about their blocks and they won't know about the world's blocks.  When the reconnection occurs several hours later the area with the shorter blockchain will be have their blockchain overwritten by the area that has the longer blockchain.  This means that the area with the shorter blockchain will suddenly lose all the confirmations that they accomplished on their own.  All those transactions that occurred while they were isolated will then propagate to the rest of the world and they will begin gaining confirmations again.

[Tesla71]

All those transactions that occurred while they were isolated will then propagate to the rest of the world and they will begin gaining confirmations again.

So that means only the confirmations are lost, not the transactions themself? So where are the informations of that transactions stored if not in the shorter blockchain?

[DannyHamilton]

. . .try to brute-force a wallet with that coins "in" it?

Think someone could tell me why that is impossible..

Private keys will not be brute-forcible regardless of how fast computers ever become unless a mathematical weakness is first found in the ECDSA algorithm used.  So long as the algorithm isn't broken, from what I've read it would require more energy to brute force private keys than the sun will provide during the entire rest of it's existence.