Comment Re:Yep (Score 1) 407
No.
I'll pick RSA 1024-bit public/private key crypto as my example. A 1024-bit key only takes 128 bytes.
Wikipedia says that 1E18 Joules is an absolute minimum for brute-forcing a single AES-128 key. (Unless you can invent an entirely different kind of computer - see quantum computers.) I'll be nice and let you do it at that cost, even though generally that would be considered impossible.
If you can brute-force 128 bits for 1E18 Joules, you only need to repeat that effort twice for each additional bit. (1024-128)*log(2)/log(10)+18 = 287.723. If my calculations are correct, that's 1E287 Joules required to brute force a 1024-bit key. Even if there's a way to speed that up 100 times, 1E285 Joules is more than a googol squared (1E100*1E100) times the total mass-energy of the observable universe.
After you've surrounded the entire universe in some kind of collector and annihilated all matter inside it to power your key-cracker, you'll have cracked just 297 bits!
Now I've hand-waved away a lot of multipliers that would actually affect your choice of implementation but the fact stands: no, the encryption cannot be brute-forced with "enough hardware and time."
I'll pick RSA 1024-bit public/private key crypto as my example. A 1024-bit key only takes 128 bytes.
Wikipedia says that 1E18 Joules is an absolute minimum for brute-forcing a single AES-128 key. (Unless you can invent an entirely different kind of computer - see quantum computers.) I'll be nice and let you do it at that cost, even though generally that would be considered impossible.
If you can brute-force 128 bits for 1E18 Joules, you only need to repeat that effort twice for each additional bit. (1024-128)*log(2)/log(10)+18 = 287.723. If my calculations are correct, that's 1E287 Joules required to brute force a 1024-bit key. Even if there's a way to speed that up 100 times, 1E285 Joules is more than a googol squared (1E100*1E100) times the total mass-energy of the observable universe.
After you've surrounded the entire universe in some kind of collector and annihilated all matter inside it to power your key-cracker, you'll have cracked just 297 bits!
Now I've hand-waved away a lot of multipliers that would actually affect your choice of implementation but the fact stands: no, the encryption cannot be brute-forced with "enough hardware and time."
