# How much stronger is RSA-2048 compared to RSA-1024?

How much stronger is RSA-2048 compared to RSA-1024? It is hard to imagine very big numbers. So what would be your way to explain the difference to someone who doesn't know much about cryptography?

• RSA-1024: no men will be able to decrypt it before the whole universe colapses. RSA-2048: even Chuck Norris won't be able to decrypt it before the universe colapses... – woliveirajr Jul 1 '13 at 16:37
• ...assuming the problem of factoring semiprimes is actually as difficult as we think it is. – Stephen Touset Jul 1 '13 at 16:55
• @woliveirajr RSA-1024 is far weaker than that. AFAIK it's currently borderline feasible to break it for state level adversaries with a few billion to spend. If it's not breakable now, 10 years from now it should be. – CodesInChaos Jul 1 '13 at 16:59
• @CodesInChaos is correct. RSA-768 was factored 4 years ago, which means semiprimes up to about 820 bits are vulnerable today. Faster hardware, etc. There's a chart somewhere that shows exactly how many bits are safe as a function of the year... Let me see if I can dig it up and make an edit. – pg1989 Jul 1 '13 at 18:29
• I heard that they could factor RSA-1024 bit in a year, with just a milion dollar computer. That why you need at least 2048 bit nowadays. – user27296 Jul 1 '13 at 20:50

• Someone who does not understand encryption, will not understand anything about GNFS either... You forgot to explain why we can't just say that $2^{2048} = 2^{1024}·2^{1024}$ is $2^{1024}$ times harder than $2^{1024}$. I heard that you could factor $1024$-bit RSA in a year with a milion dollar computer. – user27296 Jul 1 '13 at 20:53
• @user27296 I edited your comment to use MathJax formatting instead of HTML (which doesn't work in comments). I used $2^{1024}$, for example. – Paŭlo Ebermann Jul 2 '13 at 7:28
• @user27296 it's implicit in Reid's answer. It's not $2^{1024}$ times harder because GNFS can attack it faster than simple brute force. It's $2^{32}$ times harder, as mentioned. – Conrado Jul 3 '13 at 11:56