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Quantum Spookiness
and Your Database(s)
Presentation by Lewis L Cawthorne
1
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 Principle
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•No-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?
| Cat > = ( 1/√2) | Live > + ( 1/√2) | Dead >
http://www.informationphilosopher.com/solutions/experiments/schrodingerscat/
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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 sphere
More 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 matrix
A 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 space
Quantum 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) Entanglement
2) Quantum Teleportation
3) 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 sidechannel 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 area
http://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 QUANTUM
In 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.6
2. http://www.wired.com/politics/security/commentary/securitymatters/2008/10/securitymatters_1016
It may be Wired.com, but it is also Bruce Schneier
3. “Quantum cryptography conquers noise problem”, Zeeya Merali
4.
5.
6.
7.
Nature doi:10.1038/nature.2012.11849
http://www.idquantiue.com/
http://www.raytheon.com/
https://www.networkworld.com/news/2007/101007-quantum-cryptography-secure-ballots.html
“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/
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