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1024-bit RSA keys In Danger Of Compromise?
antiher0 writes "According to an email from Lucky Green that came across bugtraq yesterday, 1024-bit encryption should no longer be considered pristine. Bernstein released a proposal that outlines the creation of a machine capable of breaking 1024-bit crypto on the order of minutes or even seconds for the measly cost of ~$1B USD. For a more thorough discussion, check out the original email."
Update: 03/26 03:16 GMT by T : And don't forget to revisit Bruce Schneier's analysis of Bernstein's claims, which cast doubt on the practicality of breaking such large keys anytime soon.
It *is* a measly sum - as the email says - how many government agencies have this sort of funding? More than just a couple of US agencies that's for sure.
Assuming the email is correct (and having read it, it does't seem to be that incredible) That $1B investment gets you the infrastructure, systems and processes to routinely break 1024 bit keys (and therefore the contents of the encrypted payload) in a fairly short order.
Since many people believe that a 1024-bit key is essentially uncrackable today, tomorrow and next century, 1024-bit keys are still going to be popular.
If an organisation can amortise the cost over 3-4 years (which is the likely life of short (1024 or smaller) keys). That gives you quite a return on investment.
If that $1B allows you to break one key every 5 minutes, over a 4 year period, you can break ~420,000 keys - which works out to a cost of less than $2500 per key. If you can intelligently target who's keys you wish to compromise, the benefits could be significant.
Fast, cheap & reliable. Pick two.
That intro is deceptive at best and is, well incorrect. Remember DES and other symmetric ciphers that currently use about 128-bit or so encryption are unaffected by this. Certainly, 1024-bit symmetric encryption (your typical secret password encryption) is going to be unbreakable for centuries based on current predictions. The intro should read asymmetric or public key encryption at 1024-bits
Secondly, the advances being talked about are in factoring large numbers into their prime factors using the Number Field Sieve (NFS). This algorithm is the most advanced known factoring algorithm and if you believe the article improvements show that factoring 1024-bit length primes is doable for 1 billion dollars or so. (It was only a few years ago this kind of cost was attached to building a DES cracking machine... today I could probably crack DES on my uni computers given the software. 1024-bit factoring is only a matter of time before it is easy). However, not all public key schemes rely on the difficulty of prime factoring. Elliptic curves rely on a different hard problem
Conclusion, the intro should read "1024-bit asymmetric encryption that relies on the difficulty of prime factoring (e.g RSA) should no longer be considered pristine"
Ah... the old security through obscurity notion. Someone else can carry the debate here but trying to get security by trying to hide what layers of algorithms you are using is defeating the point of security research. A "secure algorithm" is basically one such that it does not matter whether the hacker has access to the algorithm or not. Cracking a "secure algorithm" should be as hard as cracking by brute force. If your security relies on obscurity, then you are asking for trouble in general
As for layering in general. Well it works for the most part (e.g 3DES) although there are caveats (2DES would not be safe). But the real point is that layering is slow. Doing 1024-bit RSA encryption is slow. And try generating a 2048-bit key instead of a 1024-bit key. It takes ages (possibly minutes on some computers). You may be increasing security but decreasing performance.
Now going back to the first point about a "secure algorithm", you are better of say doubling your key size and exponentially increasing the keyspace on your existing algorithm then either inventing your own layering scheme that may or may not work AND will be slow nad memory wasteful by using many algorithms. The short answer is, you don't need layering, just make larger keys.
Actually Bernstein says that he does not expect his factoring device to have any significant speed advantage over other factoring techniques for "short" keys, "short" being significantly more than 1024 bits.
The reason is that the speed up is asymptotic with a suspected slow convergence.
But I agree that for security critical application 1024 bits is too short, even if only because there is not enough safety margin.
Find the paper by D.J. Bernstein here.
Most ACs are not even worth the keystrokes to insult them. Be generically insulted and ignored otherwise.