Quote:
Originally Posted by kdusr
is that possible to brute force crack the private key with a powerful machine
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Baring a breakthrough in quantum computing or cryptography, no one is going to be brute forcing 2,048-bit keys anytime soon. Consider that there are hundreds of billions of dollars of bitcoin sitting behind 256-bit keys, and no one is walking off with those yet.
But it's not impossible either. A 1,039-bit integer was factored with the special number field sieve using 400 computers over 11 months back in 2007. Which would be roughly equivalent to breaking a 700-bit RSA key. And targeted attacks like the Logjam attack can seriously compromise key strength in certain scenarios.
Breaking 1,024-bit keys is thought to be within reach, possibly already in hand for the NSA if they have classified knowledge of algorithmic weaknesses. 2,000 qubit quantum computers are now available as well and some think this will lead to exponential gains in computational power.