Quote from: DeathAndTaxes on March 10, 2014, 04:18:43 PM

Quote from: kuroman on March 10, 2014, 04:10:16 PM

I don't understand how people claims that it will take thousands of year to crack the private key of a wallet. While yes with today computers or even clusters, it will take a thousands of years, I'm pretty sure that in a 20 years from now it will be a matter of days if not hours.

You (like most people) have difficulty grasping how large 2^256 is (or even 2^128 which is the effective security of 256 bit ECDSA keys). The 128 bit or 256 bit seems deceptively small. Nobody credible is saying classical computers could brute force keys in thousands of years..... it would be billions of years using all the energy of our sun. That also assumes you have a perfect computer.

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This without taking into consideration, alghorithms breakthrough or technological ones such as Quantum computing, hybrid system or even on the basic level, moving from Silicon to graphen would have a huge impact!

None of those (except QC) would do anything more than switching from a teaspoon to a bucket when trying to empty an ocean.

The only way a ECDSA private key will be successfully attacked is:
a) The private key isn't random enough (insufficient entropy due to flaw in PRNG)
b) ECDSA is cryptographically weakened/broken.
c) It becomes possible to build a QC with the tens of thousands of qubits necessary to implement Shor's algorithm against a 256 bit ECDSA public key (and public key is known).

Care to give us a layman's explanation of Shor's algorithm? Also, I thought the public keys were the same as the bitcoin address?
thanks!