RSA-576 Factorization Officially Announced

product byproduct writes "RSA Security finally has a news item about the December 2003 factorization of RSA-576. (See earlier Slashdot coverage). We now know what the computational cost was: the 174-digit number was factored "using approximately 100 workstations in a little more than three months"."

Comments

Lots of hardware...

[basil montreal]

That's a ton of computer hardware to use on factoring... I wonder why they didn't just use a distributed system (like seti@home) to do this... at least it's free.

Re:Lots of hardware...

[ezzzD55J]

Because it's difficult to efficiently parallelize (distribute) the factorisation algorithm, especially the final step which so far has always happened on 1 machine. In fact, if you can paralellize the final step of the GNFS (general number field sieve is generally used for these factorisations), you have yourself a PhD. thesis (in math and/or CS), I remember reading in sci.crypt.

Still safe for a while

[BuddieFox]

We should still be reasonably safe using the RSA-algorithm for a while more since the number is the equivalent of a 576-bit key. Most cryptography programs support upto 4096-bit keys, and the strength of a key increases exponentially for every bit if my memory does not fail me (correct me if it does).

Safe, that is unless someone invents quantum computers and makes them easy to produce.. :)

Re:Still safe for a while

[Ckwop]

Also remember the moore's law doesn't apply to factoring algorithms.. This is because for the GNFS the *memory* speed is what's important and that isn't growing nearly as quickly..

Not convinced? Look at the linear proportionality in this graph

Simon.

Re:Still safe for a while

[Ckwop]

Wow nice random word generator.. Can I have a go?

Seriosuly, It's utter rubbish. I mean please explain to me how you stack an S-box into a corner of a cryptographic chamber..

It's just a substitution you muppet.. And cryptography isn't all hardware speed.. I mean WEP

was broken with trivial computing power!

Simon.

Re:Still safe for a while

[thedanc]

Bear in mind, using bits to exponentially increase cryptographic strength only works until you reach the Berenstein factor, which is a practical limit on the number of S-boxes that can be stacked in any particular corner of the cryptographic chamber. After a certain point, which varies according to the chamber ceiling, it is possible albiet less space efficient to take advantage of parallel stacking to some extent.

Mods -- how could you let this get modded up? First, S-boxes are in DES, not RSA. Next, even if the random reference was to the correct cryptographic algorithm, the rest of the comment still makes no sense at all.

C'mon people, post if you have a clue, and only if you have a clue.

Re:It has to be asked...

[lewko]

No.

It tells us HOW MANY machines we need to throw at the challenge.

The whole key to protecting information is to make it cost more to recover the information than it is worth.

For example, if information is going to need to be kept secret for twenty years, projects like this help you learn based on current technology, how much crypto is sufficent (or overkill).

Security

[nuclear305]

Of course, the whole idea behind key strength is rather moot if the user gets careless with his keys/passphrase.

Unfortunately, crypto is only as strong as the user(weakest link)

While it's not always comforting to know these things can be factored, at least we can take comfort in knowing that *most* hackers/spooks don't exactly have a 100 node server farm laying around just dying to crack your keys.

Of course, unless you're the NSA and measure their servers by acres...

Re:Security

[CoolGopher]

we can take comfort in knowing that *most* hackers/spooks don't exactly have a 100 node server farm laying around just dying to crack your keys.

Of course, unless you're the NSA and measure their servers by acres...

Or if you grabbed the source for the latest windoze worm and modded it to bruteforce keys in addition to spreading...

I have a suspicion that doing that would give you a supercomputer that quite possibly ranked #1 on the supercomputer charts, and for free to boot*.

*) Comes with complimentary government provided lodging and meals.

Hundred computers * 3 months

[Gopal.V]

That makes it 240000 computer hours ... too cheap .. Think about this :

"Toy Story 2" had about 800,000 computer hours worth of rendering.
"The Hulk" had 2.5 Million computer hours
My office has nearly 400 fast machines , imagine this running them makes it 25 days . Running that every weekend makes it 12 weeks or 3 months ... It's a weekend job if I can sneak this in as along with the next upgrade.

DDoS time is over with all networks being careful about... the next big windows worm will be a distributed processing program :)

Re:Factoring in advance

[tadmas]

You won't know the number you need factored until you intercept or steal the encrypted data.

You don't have to steal anything. The number to factor (the modulus) is given away as part of the public key.

organise a database of the results but the storage - even if you just store some sort of clue to the primes used - would be staggering, even for just 1024-bit RSA.

For 1024-bit numbers, the factors will be on the order of 512-bits. The density of primes is rougly 1/ln(n), and ln(2^512) is about 355, so you should expect around every 355 numbers to be prime. That's only 3e151 numbers, not to mention that you'd have to figure every product of the two, which is 0.5*(3e151)^2, or 7e302 numbers.

Staggering doesn't begin to describe how many of these things you'd have to store.

Why waste all the CPU power?

[tangent3]

There's a far easier way to crack the the key

Jens Franke

[greppling]

(As far as I understand, he and Thorsten Kleinjung wrote most of the software used, and did most of the work in the project, while the other institutions were rather donating computing time.)

I happen to know him a little, as one of my friends is his student, and another one was. If you think mathematicians are crazy, Franke is more than that. When you talk to him, he will usually just continue to stare at the piece of paper he has directly in front of his eyes (Nobody knows why he isn't wearing glasses.) and think of that as a normal way of communicating. His office consists of 3 huge desks (plus a computer desk); on each of them there is huge bunch of completely unorganized papers lying around, mixed with empty yoghurt cans.

His mathematical skill is enormous, he has done research in quite a lot of different areas of mathematics (analysis, algebraic geometry, algebraic topology, category theory), but he never bothers at all with making his results well-known. (In fact, at least one time he actually had to be persuaded to even publish his result, which got immediately accepted in Inventionaes, the most highly regarded journal in pure mathematics.) He even couldn't be bothered to apply for a much better-payed position at another university in Germany when he was almost urged to do so.

Anyone who knows him will burst out laughing when he reads that he supposedly said "I'm very proud of all these individuals from around the world and their efforts to solve this first factoring challenge." and all this other stuff in that paragraph of the article. I bet the author of this press release desperately tried to get some phrases longer than 5 words out of his mouth, gave up, and then decided to just make up all the quotes.

Now with his mathematical skills, number factoring is (in his own opinion) a rather dull activity. The reason he is doing this is that he expects an economic breakdown soon, and he thinks of his knowledge in number-factoring as an assurance against the coming job crisis. (Of course, his position is guaranteed by the German state until his retirement.)

But if you manage to get along with him, he is actually quite nice and extremely helpful.

Memory speed vs. CPU speed increases

[billstewart]

You missed his point, though perhaps he could have expressed it more clearly. Many applications are CPU-bound, some are memory-size-bound, some are memory-speed-bound.

• CPU speed has been doubling pretty fast, every 1.5-2 years.
• Memory size (or at least, size/price ratio) has been growing pretty fast.
• Disk capacity has been booming faster than CPU speed, though disk seek times have been changing much more slowly.
• Memory speed has been lagging - I forget the exact numbers, but some of the hashcash folks did some research and found the speed doubled every N years, maybe 3-4. Certainly not the same curve as CPU speed.

If the real constraint in GNFS is storing and retrieving data, not multiplication speed, then you could easily get an environment where memory speed increases are the gating factor for your Moore's Law growth, no CPU speed increases, so your K-bit key is good for 2-3 times as many years as you'd expect.

On the other hand, factoring is a problem where the increases in Algorithm Speed have been just as critical as increases in Computer Speed. So maybe GNFS has reached the point where it's computer-speed-bound, but next year's Super-Duper-Number-Field-Sieve may be several times more efficient than GNFS, just like GNFS was several times more efficient than NFS in the ranges that are now interesting. Sometimes this happens just because mathematicians keep doing new work, and sometimes it happens because computer capacity (e.g. memory size) grows enough from Moore's Law that algorithms which weren't practical in the past become practical. There were factoring tools that weren't useful when most computers had 128MB of RAM, but work fine now, and there may be tools that aren't practical when most computers have less than 4GB of RAM, but five years from now your SonyNintendo box will have enough RAM to run Sieve@Home.