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Quantum Spookiness and Your Database(s)

Presentation by Lewis L Cawthorne

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Quantum Mechanics

1) Quantum mechanics is weird (weird==very non-intuitive)

2) If I could leave it at that, I would... But we have some (FUN!) background to dive into

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Basis of Crypto

1•Heisenberg’s Uncertainty PrincipleHeisenberg’s Uncertainty Principle1•Heisenberg’s Uncertainty PrincipleHeisenberg’s Uncertainty Principle

2•No-cloning TheoremNo-cloning Theorem2•No-cloning TheoremNo-cloning Theorem

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Heisenberg Who?

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Heisenberg What?

• Uncertainty was apparent in the earliest mathematical equations of quantum physics. Experiments confirmed that it was a feature of the physical systems and not merely a trick of the math

• Uncertainty is a fact about nature inherent in all wave-like systems, and not merely an artifact of our limited measuring capabilities

• This and the Observer effect ensure that no one can measure a quantum system without disturbing it in a manner that other parties can detect; which is awesome for cryptographic key distribution

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Schrödinger's Cat

Image from dantekgeek

on Flickr

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Super (position) kitty kitty kitty?

http://www.informationphilosopher.com/solutions/experiments/schrodingerscat/

| Cat > = ( 1/√2) | Live > + ( 1/√2) | Dead >

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Superposition!

A quantum particle exists partly in all of its theoretically possible states until we measure it. At that point, it takes on and remains in the state in which it was measured.

A “cat state” is an ‘entangled’ system where your final measurement will result in all 0 or all 1 with a 50-50 chance. Such a “cat state” with involving multiple qubits could be described as follows:

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Qubits

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Bloch sphereMore visually for |0>, |1>

and standard complex

coefficients, we have all the possible

states:

A classic bit could be

though of as in the |0> or |1> state. A qubit can be anywhere on the surface.

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The Superposition

Pure State: Mixed State:We represent a mixed state as a 2x2 matrixA mixed state is a point inside the sphere

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Collapsing It

• One cannot completely determine an unknown quantum state without disturbing the quantum state

• Disturbing a quantum state irreversibly “collapses the superposition”• Until you measure, the system can be thought of as a probability

distribution• After you measure, it is a pure value

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Hilbert Spaces

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Hilbert Info

Putting things further into perspective with the earlier sphere.

“Pure states as rays in a Hilbert spaceQuantum physics is most commonly formulated in terms of linear algebra, as follows. Any given system is identified with some finite- or infinite-dimensional Hilbert space. The pure states correspond to vectors of norm 1. Thus the set of all pure states corresponds to the unit sphere in the Hilbert space.”-- straight out of the Wikipedia entry on quantum state

(also why I don’t have to worry about this stuff most of the time and can just play with matrices)

(Note: I happen to like Wikipedia’s wording better than any of the three books I have in arms reach)

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Basis Selection

Put simply, |0> and |1> with complex coefficients form an adequate basis for representation of the three dimension space depicted by the Bloch sphere.

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No Cloning

1) You cannot clone (make a copy of) a quantum state.

2) Any attempt to copy a state will destroy the original state.

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Wow! What Else?

Well, for today’s topic we don’t even need:

1) Entanglement2) Quantum Teleportation3) Quantum Tunneling

Although all three have their uses. Especially entanglement. It’s the key to some cryptographic protocols and many quantum algorithms. Entangled qubits are what make up a quantum register

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Why Do We Care?

1) Quantum computers can properly simulate quantum systems

2) Fourier Transforms

3) Shredding many modern cryptographic techniques Basically any based upon factoring or discrete log

4) Faster search of unsorted data

5) Quantum key distribution can occur without quantum computers!

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Cryptography

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QKD from Above

http://www.raytheon.com/newsroom/technology_today/2010_i1/feature_9.html

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Better Picture

A Multidisciplinary Introduction to Information Security, Stig Mjolsnes, Ch 5, November 9, 2011 by Chapman and Hall/CRC - 348 Pages

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Why QKD?

Dr. Vadim Makarov cryptography is the only known method for transmitting a secret key over distance that is secure in principle and based on the laws of physics. Current methods for communicating secret keys are all based on unproven mathematical assumptions.-- Dr. Vadim Makarov

http://m.techrepublic.com/blog/security/how-quantum-cryptography-works-and-by-the-way-its-breakable/7762

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Perfect? Crypto

Quantum Cryptography, or more precisely Quantum Key Distribution (QKD), is based upon the fundamental laws of quantum physics. Unlike factoring for which we have no known fast solutions but that could change tomorrow, for quantum cryptography to fall to direct attacks it would require a change in the laws of physics or at the very least prove that we have massively misunderstood them.

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Perfect? Haha..

In theory there is no difference between theory and practice. In practice there is.

-- A fun quote often misattributed to whoever the attributer’s favorite quotster might be...

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Modern Crypto Is Seldom the Breach

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Imperfect Devices

Nothing is perfect. Most quantum cryptography today relies on photon detectors. The devices have been compromised by some rather ingenious side-channel attacks. It appears that it is possible to “blind” the devices, and when done properly can cause them to not detect tampering. An interesting engineering hurdle to be overcome. Proof of concept fixes have already been developed, and next generation devices should have other flaws (or hopefully none) to contend with.

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Impractical

Distance limitations really hamper it anyway. 60 km tops was the standard. The article that led me to looking into this from the Homeland Security Wire had managed to up that to 90 km over shared optic lines concurrently transmitting other data (very impressive actually), but you could stick limited data in an armored briefcase and drive it that far. That is some awesome progress though, especially in lowering entry barriers via shared cable usage. That’s better but is it “better enough” to justify replacing existing, more flexible systems.

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Weak Use Cases

Ars Technica author Chris Lee summed it up beautifully:

“Quantum cryptography is one of those amazing tools that came along before anyone really asked for it. Somehow there are companies out there selling very high end, and "provably secure" cryptography gear, all based on fundamental principles of quantum mechanics. Yet, despite being fundamentally unbreakable, there have been quite a few publications on more-or-less practical ways for Eve to eavesdrop on people whispering quantum sweet-nothings in darkened rooms.”

http://arstechnica.com/security/2012/09/quantum-cryptography-yesterday-today-and-tomorrow/

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Doesn’t Matter

“Security is a chain; it's as strong as the weakest link. Mathematical cryptography, as bad as it sometimes is, is the strongest link in most security chains. Our symmetric and public-key algorithms are pretty good, even though they're not based on much rigorous mathematical theory. The real problems are elsewhere: computer security, network security, user interface and so on.” -- Bruce Schneier

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But It Matters

QKD is seeing use today in the financial market. Wall Street likes to trade a lot of secure info in a very geographically limited space. It could also have its uses (or already be used) in government facilities, especially those clustered around DC areas to send lots of info around securely.

Currently available methods of QKD tend to involve both special (expensive) equipment and dedicated fiber optic lines for key distribution. You could more reasonably implement a share city-wide secure communication network for example

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Major Changes?

Quantum Computing

Should we pass the hurdle of decoherence and get scalable systems, quantum computers will change certain things. From a non-scientist perspective, mainly by breaking many modern cryptographic systems.

Of special interest in a database class though is how they can help search..

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Grover’s Search

We can normally average n/2 search of unsorted data.

Grover can do the same in sqrt(n).

A definite improvement. Performance, performance, performance.

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Grover’s Search

Yes. Quadractic increase in search speed isn’t as exciting as exponential increase in speed for factoring

Yes. It requires a quantum computer

Yes. Any speedup is still really awesome considering how much data is out there and how unwieldy it can be keeping it sorted and to where you can locate what you need. (A fine reason for say, Google, to look into quantum computing should it look as if it is about to become viable

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Grover’s Search

Not only was Grover’s the first useful quantum search algorithm, it’s apparently as fast as we can expect (at least asymptotically) in the quantum computation model

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Grover’s Search

I could fill this slide up with equations, and the next, and the next. A fill a whole lecture explaining them. Just trust me that as far as we can tell, if we can get a quantum computer to run it on, we have a way to search unsorted records in O(sqrt(n))

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But...

That “if we get a quantum computer to run it on” is quite the hold up

We aren’t going to “conquer” decoherence, and we won’t see scalable quantum computers. (Just a pessimistic guess on my part)

Either way, there’s more than enough reason for the engineers to continue trying to build the things

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What Now?

QKD exists. It is out there. Let’s look at some examples!

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DARPA

2003!?

The DARPA Quantum Network In 2003, in collaboration with Boston University and Harvard University, Raytheon BBN Technologies deployed the world's first quantum key distribution network in the metropolitan Boston areahttp://www.raytheon.com/newsroom/technology_today/2010_i1/feature_9.html

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SECOQC

http://www.secoqc.net/08.10.2008

QKD Network Demonstration and conference

The first live demonstration of a working quantum key distribution (QKD) network took place in Vienna on Oct 6, 2008 in the framework of the SECOQC Demonstration and International Conference. Eight QKD-links were combined in a novel quantum-back-bone network physically deployed within a typical metropolitan area network to connect different company sites from SIEMENS Austria. Typical applications for QKD, to secure data traffic from telephony

and video conferencing, were included in the demonstration.

Note: Project disbanded in 2010

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ID Quantique

ID Quantique (IDQ) markets the Cerberis quantum key distribution server device which works to handle the key distribution needs of their Centauris AES solution. It requires an optical fiber, but other than that just handles the necessary key exchanges to make the encrypted communication happen.

http://www.idquantique.com/index.php?option=com_content&view=article&id=52

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ID Quantique

ID Quantique is based out of Geneva, Switzerland

They tend to cater to government and banking sectors in Europe, and their quantum offerings are billed as best for those seeking “uncompromised security”

ID Quantique’s Cerberis product was used to protect the ballots in the 2007 Swiss elections

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ID Quantique

QKD is a new technology and it exploits quantum physics. It is certainly complex to deploy and operate, isn’t it?

No, QKD is not complex to deploy. It has reached a level of maturity such that it only takes a typical network engineer a few minutes to install a QKD system. Moreover it can be managed using standard network administration tools. 

http://www.idquantique.com/component/content/article.html?id=105

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SwissQuantum

“SWISS QUANTUMIn January 2011 Swissquantum successfully completed the longest running project for testing Quantum Key Distribution (QKD) in a field environment. The main goal of the SwissQuantum network, installed in the Geneva metropolitan area in March 2009, was to validate the reliability and robustness of QKD in continuous operation in a network over a long time period in a field environment. The quantum layer ran stably for nearly 2 years, confirming the viability of QKD as a commercial encryption technology in telecommunication networks.”

http://swissquantum.idquantique.com

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Rumor Has It

It is believed by some that a dedicated line for QKD connects the White House to the Pentagon, along with several links to military sites nearby.

Keep in mind, it has also been rumored that as of 2000 that the government was all in on developing teleportation devices and had made progress.

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References

1. “Alternative schemes for measurement-device-independent quantum key distribution”, Ma, Xiongfeng; Razavi, Mohsen. PHYSICAL REVIEW A (1050-2947). DEC 19 2012.Vol.86,Iss.62. http://www.wired.com/politics/security/commentary/securitymatters/2008/10/securitymatters_1016 It may be Wired.com, but it is also Bruce Schneier3. “Quantum cryptography conquers noise problem”, Zeeya Merali Nature doi:10.1038/nature.2012.118494. http://www.idquantiue.com/5. http://www.raytheon.com/6. https://www.networkworld.com/news/2007/101007-quantum-cryptography-secure-ballots.html7. “A Brief History of Quantum Computing” http://www.doc.ic.ac.uk/~nd/surprise_97/journal/vol4/spb3/

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Questions?

http://gajitz.com/the-quantum-cat-is-out-of-the-bag-made-of-lasers/