## Quantum Computing Not an Imminent Threat To Public Encryption 119

Bruce Schneier's latest blog entry points out an interesting analysis of how quantum computing will affect public encryption. The author takes a look at some of the mathematics involved with using a quantum computer to run a factoring algorithm, and makes some reasonable assumptions about the technological constraints faced by the developers of the technology. He concludes that while quantum computing could be a threat to modern encryption, it is not the dire emergency some researchers suggest.

## Schneier knows his stuff (Score:4, Informative)

Practical Cryptography [amazon.com]is a friendly guide to encryption that doesn't assume too much knowledge of the heady math involved. Plus, the man invented Blowfish, one of the most popular and fast algorithms around.## Re:Schneier knows his stuff (Score:5, Informative)

Applied Cryptography [amazon.com].Practical Cryptographyis a bit too basic an overview written with a co-author.## Re: (Score:1)

Quantum computers being able to factor big numbers is the best proof I've seen that factoring is not NP complete. If it were, we could just use these futuristic quantum computers (I'm talking far-future, many thousands or even millions of qbits) to solve just abo

## Re:Schneier knows his stuff (Score:5, Insightful)

by using a deterministic algorithm. Quantum computers are non-deterministic, and that's why they can be used to factor large integers. "Check all periods of r so a^r=1 (mod N) at the same time" certainly isn't deterministic.The darned things would be like oracles, just ask them any super hard question, like how to prove Fermat's Last Theorem, and they'd just spit out the answer. The things would be like talking directly to God. Is that even remotely possible? I don't think so. Factoring numbers is just not as hard as any NP complete problem.You might as well conclude that grass is purple, for all the sense that paragraph makes.

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While solving NP-complete i

## Re:Schneier knows his stuff (Score:4, Informative)

What you described is the property "NP-hard".

For a problem to qualify as NP-complete, it is also neccessary that an algorithm that can solve this problem can also be used to solve every other NP-hard problem, with only an additional transformation of its input and output in polynomial time.

Prime factoring is not NP-complete. There is as far as I know no transformation for the input and output of a prime-factoring algorithm, that would allow it to solve other np-hard problems as well.

If prime factoring was np-complete, then since a quantum algorithm is known for it, it would be certain that a quantum computer could also solve all other np-hard problems.

As far as I know, no quantum algorithm with polynomial time has been found for any NP-complete problem. So we do not know whether a quantum computer could do this

## Factoring IS NOT NP COMPLETE (Score:3, Informative)

Read Scott Aaronson's blog [scottaaronson.com] to get a clue about quantum computing.

Also read about Schor's algorithm, which is the known algorithm to factor large numbers in log(n) time *if your quantum computer has enough entangled qubits to represent the number*. Again, though, remember that FACTORING IS NOT NP COMPLETE, only NP hard. Other NP hard problems are harder than factoring (for example, any NP complete problem

Also read about Grover's algori

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Again, though, remember that

FACTORING ISNOT NP COMPLETE,only NP hard.Wrong (emphasis mine). Factoring is in NP but not (known to be) NP complete. Which means that factoring is not (known to be) NP-Hard. (The only NP-hard problems in NP are NP-Complete problems) A more colloquial way to explain it is that NP-hard problems are at least as hard as NP-complete problems, yet factoring is "easier" than NP-complete problems.

Also read about Grover's algorithm, which is a general algorithm to solve NP complete problems, and which HAS BEEN PROVEN TO BE THE FASTEST way to solve the NP complete problem of lookup in an unordered dictionary. Grover's algorithm finds the answer in n^1/2. Obviously if the fastest algorithm to solve a specific NP complete problem is n^1/2, you cannot have a way to solve all NP complete problems in log(n).

Do you even know what you are talking about? Grover's algorithm is not used to solve NP complete problems!! You've already said it -- it's a way to look up an

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Can't we all just agree that it's reeeaaally complicated?

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You are absolutely right. I made two mistakes - first I said NP hard when I just meant "in NP". Second, I was just totally wrong - I thought factoring was kno

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I thought factoring was known not to be NP complete.

To be fair I sometimes make this mistake too :)

You may be right that unordered dictionary lookup is not an NP complete problem. I can't find any references for it either way, and certainly don't know a proof myself.

I think that "unordered dictionary lookup" simply refers to a typical linear search, like how you normally loop through an array to find a specific element. The run time complexity is O(n) which is linear (this is obvious), and hence the problem is in P. It is therefore NP-complete iff P = NP (which is speculated to be highly unlikely). Not a "proof that it isn't NPC" per se, but that's as close as you could get to a proof.

The way it can be "used" to solve NP

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I believe algorithmic complexity is rated based on the size of the input, not the size of the search space (obviously, since search space is a concept specific to this problem).

If you add one bit to the input of a dictionary lookup, it implies that you would on average go through twice as many entries to find the key, so the complexity of unordered dictionary lookup is exponential on the size of the input.

I reco

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er, of course I meant "and n is 80"

I was revising the post to find numbers that demonstrated my point, and failed to update a reference...

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I consider this a contradiction... the existence of such a computer violates my sense of reality. It is far easier to believe that factoring is indeed not quite as hard as NP-complete problems.Got a couple of spares? Your sense of reality seems to be a bit faulty. We already have seen those cut-offs before: they happened when someone decided a computer was a good enough tool to design chips instead of using pencil and paper. Anyway, this is not a mater of something being "easier to believe": either factor

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It's not hard to follow; if I give you a candidate solution to a problem and you can check quickly if it is true or not (i.e. in poly-time) then the problem lies in NP. So all problems in P lie within NP. Some problems in NP are harder t

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The name "quantum gate" is quite misleading, and that may be the reason why Mordakus mis-understand. It's actually means quantum operation. Shor's algorithm requires 72k^3 quantum gates, is means requites 72k^3 quantum operations. It does not means we need to build a q

## Re:Schneier knows his stuff (Score:5, Interesting)

Right now a lot of people working in the field say quantum computers are about 40 years off. The scary thing though is how its likely to play out. For a few decades quantum computers will likely remain "40 years off" (in the fusion sense), but then someone is going to figure out how to get the error rates below threshold, and then quantum computers will be only 10 years away. That doesn't give us much time to stop using our favorite public key algorithms. That's too bad for nTru; (they have a public key system that is likely resistant to quantum computers), their patents will be long expired.

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## The value of nTru's patents (Score:2)

It all depends on how long you need the stuff secret.

If all public key crypto except for nTru's is bust in possibly 25 years, and your stuff needs to be secret for 50, then you better be using quantum-resistant (did I just invent that term?) crypto Right Now(tm).

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That's the difficulty with predicting them.

I appreciate Bruce's attempt to predict when the X-Box's encryption (4096-bit) will be cracked. But a looksee at history shows that events happen in a funny, nearly fractal manner. Perhaps the series "Connections" would be a better description of how tech has spun up.

Here's a "predict the future" example:

The late 1938's brought research into the incredibly odd element uranium

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## Re:Schneier knows his stuff (Score:5, Funny)

Hope that clears it up for you...

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There is also, if I read this correctly, some chance that it will turn into a cat.But you won't know if it's alive or not until you look inside the box.

## Brilliant explanation... (Score:2)

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## not exactly a "threat" (Score:4, Insightful)

The day PKIs that use factoring or discrete logs become easy to crack is the day when there's going to be a lot of tremendous amount of money spent on stop-gap security measures until someone figures out something new...

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I imagine one-time pads will come back in style.

## Re:not exactly a "threat" (Score:4, Insightful)

I imagine one-time pads will come back in style.

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Well, just think about all the SSL enabled sites out there, and remember you will now have a N * N (client * server) number of relations that need to setup a symmetric key (which is what a one time pad is, basically). Also note that you don't have a certificate infrastructure, so you cannot just go to VeriSign or any other trusted third party and buy a certificate from there. You cannot download

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One-time pads cannot be reused. That's why they're called one-time

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## You have to get the pads to the other person... (Score:3, Insightful)

If you have a way of transmitting the pads securely then you could just use the same system to transmit the messages - no encryption needed!

## OTP exchange (Score:2)

Well, you could, but then you might have to

wait!You can securely exchange OTP when you're physically in the same room with someone, and then

useit when you'renotin the same room. This seems like a very reasonable thing to do with people that you know and regularly meet in Real Life (e.g. your wife).That case obviously doesn't apply with most of the people you

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Both parties need the same pad. You need to be able to ship that pad to them or hand it to them and be sure no one snooped or snoops the OTP. If the pad is compromised how do you inform the other party it has been tainted? Unless you go tal

## Secure asymmetric encryption? (Score:2)

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http://www.iacr.org/archive/crypto2000/18800147/18800147.pdf [iacr.org]

## Well, lucky for us (Score:2)

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As far as I know, it is not known whether quantum computers can solve NP-hard problems in polynomial time. To say that they fail at NP-problems may be premature.

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Well, it is conceivable that NP is solvable using quantum computers in poly time, while pretty much everyone believes that P!=NP for ordinary computors.

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If quantum computers can't solve problems in NP quickly, then presumably it follows that normal computers can't either.

This would prove P != NP, which hasn't been done. Ergo, it can't have been proven that quantum computers can't solve problems in NP quickly.

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Thanks for the laugh.

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I am not sure what you mean by a non-linear operator. Certainly there are numerous ways of approximating various NP problems with different degree of accuracy.

## There's nTru (Score:1)

## the fear (Score:2, Insightful)

## "polynomial time" (Score:4, Informative)

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## Quantum computing is no threat because... (Score:3, Informative)

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We may never have either nuclear fusion or quantum computing, as currently envisioned. As you say, it's impossible to predict. All we can say with some assurance is that we'll probably figure out

somethingthat will## Re: (Score:2)

## Encryption will move on, too (Score:2, Interesting)

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## Does exist any quantum computer proven to work? (Score:1)

1. Entanglement. Is this a fact or a theory? Looking on web I found only few experiments with some possible loopholes. I found the principle hard to grok.

2. Heisenberg principle. It mainly states that observing an object you are changing the state of the object. The Heisenberg example from wikipedia is using a photon for measuring the position of an electron and the photon is changi

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To make a long story short, though, both quantum entanglement and the collapse of wavefunctions due to measurement are experimentally-confirmed fact, and small quantum computers have been built.

## Re:Does exist any quantum computer proven to work? (Score:5, Informative)

Although QM computers do use basic entanglement for creating superpositions, understanding Shor's algorithm (the one everyone is concerned about since it's factoring in polynomial time) is mostly just understanding QM superposition. Entanglement gives generic QM computers great parallel processing power by superposition by explaining how QM probability wave combine under superposition, but Heisenberg limits the computing power of a QM computer in a non-trivial way as well because after you collapse the wave functions by measurement you give up the parallel processing enabled by Entanglement (e.g., if you peek inside the oven, it stops working, if some of the heat leaks out of the oven even with the door closed, it doesn't work as efficiently, the oven being the QM computer).

FWIW, Shor's algorithm essentially converts factoring into a sequence period finding exercise. You might imagine that that's something easy to do if you had a machine which given a bunch of superimposed waves with a certain modulo structure could tell you the period (hint the ones that don't modulo with a specific period with self interfere and measure as zero, where the one with that period with self-reinforce). With a QM computer you do this all in parallel with superimposed probability waves and when you measure it, the highest probability one you measure is the one that doesn't self-interfere (the ones that self-interfere has probability near zero). Basically this measurement is wave function collapse which doesn't actually depend on entanglement or heisenberg to understand (although it does require you to believe in QM wave functions and measurement operators).

Entanglement is really a strange artifact of QM that explains probability correlations that you see in QM experiments that can't be explained classically. It's really more of an artifact of the existance of probability amplitude waves (the QM wave function) rather than an effect that directly enables the QM computer. Of course if you didn't have QM wave functions you wouldn't have a QM computer so I guess that's a chicken and egg scenario. Entanglement is like the "carburator" function of the QM computer. The QM computer uses superposition of QM wave functions to work and when you have more than one QM wave function, they get entangled when you start superimposing wave functions and the way the waves entangle helps you compute in parallel so it's important to understand how these waves entangle.

Heisenberg's principle is a consequence of wave function collapse (measurement) which also limits the QM computer (this limiting effect is often called QM de-coherence). Heisenberg isn't required by a QM computer when it's computing, but you need to see the result somehow so when you measure the result, one of the side effects is the Heisenberg principle (although that's also a chicken-egg problem, since HP is a consequence of QM wave function collapse and w/o QM there's no superposition computing). The closest explanation I can think of is that Heisenberg's principle is the "heat" caused by friction of the QM computer. You need friction to stop the computer to read out the result, but at the same time you can't get rid of a little friction while it's running either (causing de-coherence). The side effect of this friction is heat.

You may have a personal opinion that superposition is a "nice way of doing statistics using discrete values for covering the not so discrete results of experiments", but there is experimental evidence that your personal opinions is at odds with physical reality. As QM computers that do QM computing (including IBM's NMR experiment which implemented shor's algorithm) have already been implemented it's hard to refute that something non-classical is going on.

It may be that in the end, QM is total malarky and there's some other weird unexpected thing going on, but there are mountains of evidence that whatever is going on, it isn't as simple as "hidden variables"

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My main problem stays in "continuous vs discrete" problem as you mention it. I still believe that the discrete values are just "good values" in a wave equation like "Schrödinger equation" and not really discrete. The main problem as I see it is that "Schrödinger equation" is practically unsolvable using current mathematics and finding a continuous equation is like findi

## Re:Does exist any quantum computer proven to work? (Score:4, Informative)

1. Entanglement: It is fact. If you send a photon through a certain type of non-linear crystal, two photons will emerge that are entangled quantum mechanically. To truly understand this requires some knowledge of quantum mechanics, a basic introduction to QM and entanglement can be found here [ipod.org.uk] and here [davidjarvis.ca] if you care to learn more.

2. Heisenberg principle: You inadvertently stumbled onto the problem yourself, kinda. When trying to measure the position of the electron, you use a high energy photon and this photon. When this high energy photon interacts with the electron it alters the velocity of the electron, so you know less about the velocity of the electron. When trying to measure the velocity of the electron, you use a low energy photon. This low energy photon measures the velocity well, but it moves the electron a little bit, so you don't know its position. This issue is the essence of the Heisenberg uncertainty principle.

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2. The problem with talking about quantum physics is that you deal with principles quite unlike real life. Every particle is a wave (see de broglie). It can be represented by a wavefunction, the square of which is the probability of detecting it at any given point. Different energies represent different waves, but not every wavefunction is possible. Hence, only certain energies ca

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You may be interested in Bohm's interpretation of quantum mechanics, which is much more intuitive because it deals with realistic particles travelling in a "quantum

## Shor's Algorithm (Score:4, Interesting)

If that's the case, it's probably worthwhile to discuss Pollard's Rho algorithm [wikipedia.org], which has a poorly understood worst-case complexity (as a Monte Carlo method), but has a potential average case complexity that is comparable to the quantum.

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Besides, if you believe that some method is faster in practice than what the theory says, there are some RSA challenges out there with big money prizes for you to win.

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## well duh (Score:1)

## Am I missing something? (Score:2)

## Incorrect interpretation? (Score:2, Informative)

## Botnets are more of a threat (Score:1)

## Use quantum computers to ENCRYPT (Score:2)

Why can't we use them to come up with an equally mind-blowing way of encrypting?

I don't mean single photon secure fibre channel stuff. That seems fairly impractical to deploy to the whole internet.

I mean, why can't some mathematical genius come up with a new encryption algorithm that you

can only implement on a quantum computer, and which produces a cipher text so random that it

can't be decrypted even by another quantum computer unless it knows the secret.

Does anyo

## Complete article (without subscription) (Score:3, Informative)

http://www.scottaaronson.com/writings/limitsqc-draft.pdf [scottaaronson.com]

Scott posted it on his blog on 2/18, see http://www.scottaaronson.com/blog/ [scottaaronson.com]

(The blog is often quite technical as you can expect but funny and worth following just for its non-techical bits. Circumcision and Australian models are also discussed on frequent basis.)

## Part of a long lineage of naysayers (Score:2)

Heavier-than-air flight is impossible; a train will never go faster than a person can run or the passengers will asphyxiate; there is no reason why anyone would want a computer in the home; etc. [wilk4.com]It's a bad idea to discount future technological advances wholesale.

## In what ways is this a problem? (Score:2)

I would consider that if Quantum computers exist, it would pose a serious threat to security and military applications as your enemy would always be listening. I don't know if E-Commerce would grind to a halt, since governments would initially be the only ones to afford it. I would think that instead of hitting e-commerce the better thing to

## Public key ciphers aren't used for encrypting data (Score:2)

Your encrypted files will be safe against quantum computers.

## There is a problem with this (Score:5, Interesting)

He makes an extremely cogent argument, but it is hampered by the lack of information we have about the state of the art in quantum computers.

Domestic spying is massively popular with western governments right now, and if you think that the NSA and GCHQ aren't doing secret research into quantum computers you are out of your mind. Furthermore, it is a commandment of signals intelligence that you do not let the enemy know you have broken his code - and in this case the enemy is us. We have no idea how far along they are. We have no idea what the generational length is for the quantum computers that are certainly being developed in secret.

Basically, this essay could be published and make just as much sense either before or after a critical breakthrough had been made by one of the aforementioned agencies and they hadn't told anyone. Thus, we have no way of knowing if we are already past that point or not.

Given that it has already been shown that quantum computers are not infallible, would it not make sense now to start working on encryption methods designed to flummox them?

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That is, so far as research goes. I think implementation lags the private sector by several years due to bureaucracy.

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Yeah, but who do you think made up the rule of thumb ;)

Seriously though, you can't really make that kind of prediction with such a new field of technology. It would be like trying to guess how far along the Manhattan project was as a civilian in 1942.

Whilst interesting, this guys piece is the crypto equivalent of the Drake equation; sound maths, but it doesn't tell us anything because we have no way of knowing any of the variables.

## Not Schneier's analysys but some schmuck's (Score:1)

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Yes, but what about the matters you've already encrypted? Early buzz around PGP was that it would supposedly take millions of years to decrypt even a single message. For those people who encrypted their private communications, it is a big shock that all your secrets may be read in just a few years.

## And the answer is ..Re:So how do you encript ..... (Score:3, Funny)

The best encryption is disconnection. Its unbreakable even by quantum computers to the nth power.

the next best is perhaps a sequence of seemingly unrelated actions followed by a false positive... or other such use of seemingly unrelated data/actions.

A few might remember the seemingly different things you could do to cause a developer hidden message to come up on the Amiga.

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(No need to point out technicalities. I'm joking.)