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Time Running Out for Public Key Encryption
holy_calamity writes "Two research teams have independently made quantum computers that run the prime-number-factorising Shor's algorithm — a significant step towards breaking public key cryptography. Most of the article is sadly behind a pay-wall, but a blog post at the New Scientist site nicely explains how the algorithm works. From the blurb: 'The advent of quantum computers that can run a routine called Shor's algorithm could have profound consequences. It means the most dangerous threat posed by quantum computing - the ability to break the codes that protect our banking, business and e-commerce data - is now a step nearer reality. Adding to the worry is the fact that this feat has been performed by not one but two research groups, independently of each other. One team is led by Andrew White at the University of Queensland in Brisbane, Australia, and the other by Chao-Yang Lu of the University of Science and Technology of China, in Hefei.'"
I have developed an algorithm to efficiently decrypt ROT-26. You will need to use it to read this encrypted message.
See my journal for slashdot ID's by year. Mine created in 2005. http://slashdot.org/journal/289875/slashdot-ids-by-year
It doesn't necessarily mean the end of public key cryptography, it just means we'll have to come up with something other than prime factoring to compute the keys.
What this does mean is that there's going to be a lot of money to be made replacing public-key cryptograhy in custom code ala Y2K.
My blog
http://www.huliq.com/34160/qubits-poised-to-reveal-our-secrets seems to be a copypasta of the article.
Yeah, the Chinese government is the only government that would like to do that.
I don't care why you're posting AC
The quantum computer referenced in the summary managed the immense feat of finding the factors of the number 15. While it is true that factoring numbers of the magnitude used in cryptography is now a "matter of engineering", there are profound difficulties involved in scaling quantum computing. The fundamental problem is called "decoherence" and describes the tendency of quantum systems to become entangled with their environment, and the consequent loss of pure quantum states. The issues involved in quantum computation connect to deep issues of thermodynamics and entropy, and research on quantum computation has potentially great significance for fundamental physics. Cryptography may have to develop and implement new, extended standards as computational techniques evolve, but the encryption sky is not yet falling.
...His velocity, however, is known precisely.
Can you be Even More Awesome?!
"PQCrypto 2006: International Workshop on Post-Quantum Cryptography"
http://postquantum.cr.yp.to/
From The link:
Elliptic curve public crypto does not rely on the difficulty of factorization, so this specific attack wouldn't affect it, but I don't know if there are applicable quantum computing attacks. Too bad software patents are such an issue for it in the US.
The Magic Words are Squeamish Ossifrage
Depends on the observer.
Well, it has never been successfully tested.
The thing I worry about, is, regardless of which government or group is working on it is this, if this is what they're releasing to the public, how much farther ahead are they behind closed doors.
that it will be a really long time before QC are cheaper in terms of factorizing numbers than the equivalent classical machine. If they work at all. The common beliefs about the different QC other implementations in the field usually are said to be
-NMR: Most advanced no decoherence, but severe scalability problems. Nobody knows if they can ever put more than 10 qubits (
-Quantum Dots: Nice but Semiconductors have a hell of excitaions and decoherence
-Spintronics: Interesting, but it will take a time until it is under control
-Ions: well advanced, good control, some scalability problem (not necessarily IMHO)
-Atoms: advancing (-> Atom Chip), could be fine
-Superconducting qubits: Right now decoherence problems, which may be solved.
Chinese secret services are so secret they don't even have a name. Actually, they don't even need one.
Karma cannot be described by words alone.
I finally went and figured out gpg just this week and it's already about to be obsoleted...
This sounds like some serious breathless bullshit to me.
There have been quite a few different methods of quantum computing developed that take advantage of several types of quantum processes in nature. I worked on bulk-spin-resonance QC as a research assistant at MIT.
To the best of my knowledge, every method so far developed runs into coherence and noise limitations that make it very difficult to scale them up. It's usually not too hard to build a 3- or 4- qubit quantum computer, but scaling up the size seems to itself have an exponential characteristic to the problem. Basically, it's very hard to build a practical quantum computer that works on the scale necessary to factor even modest sized numbers. The engineering challenges to make any of these methods at all practical are bafflingly hard - the underlying science and math are pretty straightforward on the other hand, and the algorithms are undoubtedly cool as hell.
I understand these days the interesting work is on trapped-ion approaches and semi-conductor approaches.
Anyway, Shor's algorithm has been around for years. The theory behind QCs is fairly well understood, the experimental difficulties are huge.
Basically, unless this represents a real breakthrough, i.e. a technique that is not just scalable in theory but can be demonstrated practically to be linearly more difficult to scale up the number of qubits, then it's not a breakthrough that anybody needs to worry about yet.
Without seeing this article's full text though, it's hard to really know, but I gather optical approaches have been tried before and haven't gotten any further than anybody else has.
Governments still use one-time pads for the really sensitive stuff.
See http://en.wikipedia.org/wiki/Numbers_station
The one-time pad is in no danger of being broken by quantum computers or anything else because it's provably unbreakable. (Unless there is operator error, and sometimes that's the case)
The Good Guys(tm) want to have this so that they know what The Bad Guys(tm) might have, and that way they can change their systems before they are cracked. I could imagine some crime syndicate paying the millions for a working quantum computer and the PhD talent to run it so that they could break into international banking systems.
On the flip side, pressing exactly two HD-DVDs with random data, and distributing these to your bankings sites for the most sensitive information is getting more and more cost effective.
All ideas^H^H^H^H^Hprocesses in this post are Patent Pending. (as well as the process of patenting all postings)
Does anyone know the name of the Chinese equivalent of the CIA, KGB and MI6?
Jet Li.
Right! Well, them and a former college age hacker turned Mob IT manager turned world saviour.
Think of it Marty. No more rich people, no more poor people, everybody's the same
*sigh*
This doesn't break "public-key cryptography". Even if you could build a Shor-factorization machine big enough to use against real-world keys (and that's a *big* if), it's only good against RSA. Elliptic-curve cryptosystems, for example, would be entirely unaffected. In general, the question of whether general-purpose quantum computers would break all public-key cryptography is a really hard one. It's equivalent to whether there are any trapdoor one-way functions which are in P but with inverses not in BQP. Even the existence of non-trapdoor one-way functions is still an open question; they would have to have inverses in , and proving that would also imply P != NP. All the existence of Shor's algorithm really shows about that problem is that there is at least one problem, integer factorization, which is in BQP but (probably) not in P.
Anyway, it's a long way from running Shor's algorithm to factor 15 to being able to factor a 4096-bit RSA key. Remember that because of the no-cloning theorem you can't build a flip-flop for qubits, so quantum circuits are all combinatorial logic. Applying Shor's algorithm to real-world RSA keys would require building a complete modular exponentiator combinatorially out of quantum logic gates, wide enough to deal with the biggest key sizes practical for anyone to use (and the cost of RSA encryption/decryption only scales linearly with the key size). We couldn't even build that out of regular non-quantum logic.
Encryption/decryption grows linearly in the length of the key
No. With classical algorithms, RSA encryption and signature verification are O(n^2), while RSA decryption and signing are O(n^3).
and cracking is [considered] exponential in the length of the key
No. All modern factorization algorithms are subexponential; this is why a 1024 bit RSA key is roughly as secure as an 80 bit symmetric encryption key.
Tarsnap: Online backups for the truly paranoid
Although you are theoretically correct what you have said is wrong in practice. If I want to run a classical algorithm on a larger piece of data then I can just simulate a larger computer (to the extent that I page things in or out of memory, implement 64bit operations in 32bit etc). For a quantum computer I need a bigger computer. I can't simulate a 8-qubit machine on a 4-qubit machine with just a polynomial slowdown.
:)
I can't read the actual article at home so I don't know how large their machine is. Shor's algorithm has actually been run on a 4-qubit machine before so the summary is incorrect. I believe that the number they factored was 15. The point being that I need a quantum machine large enough to factor the RSA number. As building a 8-qubit machine is not as simple as slapping two 4-qubit machines together (because of problems with quantum coherence) there will always be a state-of-the-art for how large a Quantum Computer can be, and public crypto with keys significantly larger than that will be safe until a larger machine is developed. Sort of a faster version of the battle between cryptographers and cryptoanalysts that we see at the moment.
You'll notice that nobody made the same claims when EPFL sieved a 1024-bit number recently - instead everyone said use larger keys. The situation is likely to be the same as Quantum Computers increase in size. Lastly, not all public key crypto is shafted, only things that rely on factorisation as a problem. ECC will be quite safe until (if?) somebody develops a quantum algorithm for discrete logs.
Disclaimer: I don't do research in quantum - I work in cryptography, but the quantum guys have an office down the corridor and occasionally I understand what they are talking about. Ashley, don't beat me around the head for getting the details wrong
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The whole point of a One time Pad is that there is no such thing as an algorithm to crack it without quite some information in addition to the ciphertext. The beauty of a One Time Pad is that you can crank through every possible key, but that doesn't get you anything. Sure, you may wind up with some keys that take the ciphertext and make perfectly intelligible English out of it, but there are an enourmous number of messages of a given length, and any of them could be an equally valid. So, cracking a message properly encrypted with a OTP basically amounts to creanking through every possible bit combination the same length as the message, and then guessing arbitrarily which one is the "solution."
In practice, the only time OTP's get broken is when they are used wrong. For example, a message is enciphered with a particular pad, transmitted, and then through a beaurocratic fuckup, the same message also gets transmitted as plaintext. Then, somebody fucks up and uses the same OTP (now a TTP!) on another message. the cryptanalyst gives the old captured OTP a whirl and gets lucky. The OTP is only vulnerable to the CHF algorithm. (Cascading Human Fuckups.)
For the best known classical factoring algorithms, doubling the key length will basically multiply the number of operations required to factor by itself. For Shor's algorithm, doubling the key length might multiply the time to factor by four, but given how quickly computers get faster, that's basically worthless.
That might be theoretically true, but in practice public keys are in use for YEARS (if not decades).
Example, vising gmail and checking out the certificate Google (which is pretty security conscious) has a key valid from 05/03/2007 through 05/14/2008 (over a year).
In order to trivially look at EVERY session encrypted over gmail an attack would need to crack that key ONCE. Google is pretty good by the way, there are certs in existence for far longer than 1 year out on the intraweb.
It is true that every session uses a symmetric cypher with a different session key... but how do you think the keys are exchanged? Once the PKI encryption is broken, the attacker will be able to read the session key in plaintext and decrypt the entire session. And this is for every single person using Google's certificate. That is why cracking PKI is so profitable, the long-term nature of the keys means once it is cracked, you have free reign for a long time.
AntiFA: An abbreviation for Anti First Amendment.
There seems to me some (a lot?) of FUD mixed up in this article. (surprise surprise...)
:-) i'm down with that.
It starts out with the fact that public key encryption relies on the existence of one trapdoor one-way functions. Now in practice we mainly instantiate these functions with the RSA function (f_e(x):=x^e mod n with trapdoor p,q such that pq=n). But there is no reason to believe this is the only possible example of trapdoor OWF! Admitedly in the 80s when this concept was first being explored there were quite a few failures when trying to base implementations on NP-Complete and/or NP-Hard problems (think knapsack for example). But since we already had RSA with all it's nice properties (efficiency, elegance and simplicity) the research community was not overly motivated to find others.
There have been and to this day still are other lines of research. Take Ajtai and Dwork's work in the direction of basing PKE on worst-case hardness of the shortest vector problem (SVP) or Micciancio's work on generalizing the knapsack problem such that average-case hardness of approximating the answer can be reduced to worst-case hardness of certain lattice based problems.
Another general direction has been to come up with groups and fields over which solving the DLP is difficult. (For example torus-based crypto and generalized Jacobian groups). AFAIK for most of these candidates there are no (known efficient) reductions from the DLP problem over Z_p or elliptic curves to the DLP in these new groups. Thus it is not immediately clear how or if Schorr's algorithm would break such systems.
In any case there is reason to believe that there can not be (or that we can't find) good candidates for trapdoor OWFs in the quantum computational model. After all there is such a thing as Quantum P and Quantum NP. Though the inequality of these set's of problems doesn't directly imply the existence of quantum trapdoor OWFs it is a good indication there of.
So basically the message is : Relax! The PKE world is by no means on the brink of an apocalypse. At most (and best in my opinion) we're in for a bout of some serious foundations research. to me that just sounds like more funding for applied mathematicians and complexity theorists from various corners and a WHOLE bunch of new candidates and interesting results.
Cheap storage will eventually destroy any kind of crypto/anti-crypto technology.
What are the new DVD formats getting? 50GB of data RW? Will options up to 250GB or so of RW storage?
How much information do you really, really need to hide, anyway? Maybe a couple of megabytes of financial-related data per day? A one-time pad on a DVD should provide you with centuries of totally secure communications.
So you sign up for your bank account. The bank snail mails you a 10GB random noise memory stick. You add it to your 10TB secure random storage system and you and the bank can talk for the rest of your life without anybody else being able to listen in.
Generating the assymmetric keys takes time, that's why you use symmetric keys for real time encryption. So changing the assymmetric keys too often is unfeasible right now. You want them to be valid for a longer time than just a few seconds.
It's been a while since I looked at Shor's algorithm, but I was under the impression that you needed a quantum computer with a number of qbits greater than or equal to the key length in order to get that kind of scalability with the algorithm. Due to entanglement problems, building a quantum computer with a sufficiently large capacity to run Shor's algorithm on keys of a useful length is still very hard. We've had quantum computers that can use it to quickly factorise trivial keys for a while now, but making bigger ones is very hard.
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I am a professional research cryptographer. There are many misstatements in the comments so far (what else should one expect, it's Slashdot.....)
Here are some facts to fix the clutter:
1. Shor's algorithm works on quantum computers and can factor integers in polynomial time. This breaks all public-key systems that depend on the hardness of factoring, including RSA, Rabin, Paillier, and XTR.
2. A different version of Shor's algorithm also computes discrete logarithms (again, in poly time). This breaks all public-key systems that depend on the hardness of discrete log, over *any* cyclic group. This includes ElGamal, even over "exotic" groups like those associated with elliptic curves.
3. Nevertheless, factoring and discrete log are different beasts and are not known to be equivalent to each other. Still, Shor's algorithm (in different versions) solves them both.
4. Shor's algorithm does not yet break all known public-key cryptosystems. Systems based on lattices, for example, do not appear to be affected as of yet. These include Ajtai-Dwork and a couple systems by Regev. NTRU is based on lattices, but is based on some not-so-natural assumptions (i.e, the assumption that "NTRU is secure").
5. Public key encryption is (probably) *not* equivalent to trapdoor permutations (or even trapdoor one-way functions). TDPs are a much stronger notion and are not strictly needed to do secure public-key encryption. For example, ElGamal and lattice-based systems are not based on trapdoor primitives per se.