Practical quantum cryptography
Save This Post as PDFAs it seems, people from Cambridge were able to overcome difficulties that make quantum cryptography impractical: they have built a network with quantum cryptography-based security that allows 10 Mbit/s broadband speed (although the distances between nodes cannot exceed 10 km) – previous speed record was something like 10kbit/s or so.
Open key cryptography
In order to understand what does gibberish above really mean, let us recall some basics of public key-open key cryptography. Suppose we have a large number N which is a product of two primes p and q. We will call the number N a key. In the simplest case the key is known to everybody – to the sender (Alice), to the receiver (Bob) and the hacker 
(Eve). The sender encodes information in some way, and in order to decode it, one has to know the value of q. If Bob knows p (the secret key), Alice can send him encoded data and open key N=pq, and Bob will easily calculate q.
If Eve wants to hack the code, she will have to learn the value of q somehow. In order to do that, she will have to express the open key N as the product of two primes – this procedure is known to get harder and harder while N becomes larger and larger. In principle, we can choose N to be so large, that contemporary computers will need time of the order of the age of the Universe to expand N.
Open keys and quantum mechanics
In 1984 Charles Bennett and Jiles Brassard have introduced a certain modification of the algorithm above called BB84. In order to increase security provided by the algorithm, the modification involved the use of quantum mechanics (in particular, a property for the wave package to reduce due to the very process of measurement). In Bennett-Brassard approach, the number q is not known at the beginning at all. Alice sends a sequence of photons to Bob, these photons being polarized in the two special basis. Usually, these basis are denoted x (vectors of the basis are oriented diagonally, at 45 and 135 degrees) and + (vectors of the basis are oriented horizontally and vertically, at 0 and 90 degrees). Bob and Alice know the choose the polarization prescription in advance – for example, that horiztonal polarization in the basis + means 0, while vertical polarization means 1. It is not known a priori in which basis a given photon will be polarized – a random number generator decides that.
Bob is trying to detect polarization of the incoming photons. If his guess regarding the choice of basis for the particular photon is wrong, the result of his measurement will be random. Detecting a sequence of photons of a certain length, Bob constructs what is called a primary key. Then, using an non-encrypted channel, Bob reports to Alice which basis he used to detect the polarization of every given photon in the sequence. In turn, Alice tells him whether his guess was correct or not. If his guess was correct, Bob saves the result of measurement, otherwise he erases it. Alice does the same. As a result, both Bob and Alice get keys of the same length.
The last stage of the algorithm is checking out how safe is the key. To check this out, Bob and Alice choose randomly several bits from their keys and compare them using un-encrypted channel. If Eve (hacker!) was listening the full transmission, it should have influenced the polarization of photons sent. This in turn should lead to a very large number of discrepancies between Bob’s and Alice’s keys. If the number of discrepancies is larger than a certain threshold value, the channel is declared to be unsafe – Bob and Alice will have to start from the scratch.
Open keys + quantum mechanics -hackers
Theoretically, BB84 allows to construct absolutely safe network. In reality, certain complications may appear. Here is one: Alice should send a single photon after photon to Bob, in reality, this is almost never so – impulses she sends contain more than one photon. This gives Eve a chance: she detects impulses containing more than one photon, picks one from the impulse and sends the remainder to Bob. Then, listening to the conversation between Alice and Bob, she is able to recover most of the information. This is called photon-number splitting (PNS) attack.
Another difficulty is the speed that network secured with quantum cryptography allows for – as was said above, the maximal throughput people were able to achieve so far was about 10 kbit/s. That’s what makes the work of people from Cambridge revolutionary.
What did they do
They have constructed a network with throughput about 10 Mbit/s, and what is even more important , cheap one.
They use somewhat upgraded BB84 featuring a trick: intensity (that is, average number of photons) of some of the impulses is specially made lower. Alice tells Bob which impulses were low-intensity ones, and Bob calculates the throughput of the channel. If Alice and Bob somewhat fine-tune parameters of the transmission and throughput of the channel, they will find significant drop in throughput if the network is under PBS attack.
Current in avalaunche photodiode as a function of the number of photons. From the paper
Second improvement is that they use avalaunche photodiods (see the plot above). This is what allows them to increase the frequency in the network to 1 GHz (corresponding to 10 Mbit/s over distances up to 20 km).
Via lenta.ru.
Literature:
1. N. Yanofsky, Quantum cryptography for computer scientists
2. Dirk Bouwmeester, The Physics of Quantum Information: Quantum Cryptography, Quantum Teleportation, Quantum Computation
3. Simon Singh, The Code Book: The Science of Secrecy from Ancient Egypt to Quantum Cryptography
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Dynamical maps
… in continuation to the Sunday’s post about dynamical visualization – sorry, cannot wait before the next Sunday to post offtopic
Just discovered another beautiful tool for a curious mind via Sergey Schegloff – press “Play” and enjoy the movie about the history of religions:
As it seems, Islam was always a very serious player with strong base, while Christianity is more like a recent fashion. In order to change this impression, maybe the density of population should be taken into account.
More interesting maps (“March of Democracy” etc.) can be found on the “Maps of war” website.
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Witten interviewed by Ira Flatow on Big Ideas: video of the day
.. and a very clear introduction into string and M-theory for dummies
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Fermi telescope does not confirm DM claims
Fermi Space Telescope (image by NASA)
Fermi gamma-ray space telescope was unable to predict the presence of the 300-800 GeV peak in the distribution function of high energy electrons in cosmic rays. Let me remind you that the anomaly we are talking about was claimed to be found by the ATIC team and generated recently a lot of buzz in high energy physics community (one source of those high energy electrons may be decay of dark matter particles).
It is interesting to note two things in this respect:
a) “Fermi” detected about 4 million events in the corresponding window of energy, while ATIC – only some hundreds of thousands. Can the excess that ATIC have seen be related to some effect in the atmosphere? (just kidding)
b) On the other hand, “Fermi” detectors are actually less sensible in the 300-800 GeV window we are interested in than ATIC detectors, that is, we naturally may expect to find bumps in “Fermi” data where ATIC has seen a well expressed peak. Some people say that indeed see those bumps
c) ATIC team is not the only one who claimed they’ve detected the anomaly – PAMELA has also seen some increase in ratio of positrons over electrons at lower energies (and PAMELA is also the space mission).
Update: the paper by Fermi/LAT collaboration is online: “Measurement of the Cosmic Ray e+ plus e- spectrum from 20 GeV to 1 TeV with the Fermi Large Area Telescope”.
So, it seems we have quite a controversy here
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387. Gapminder and dynamical visualization
Nowadays, in statistical analysis of various economic or social factors we mostly use plots where time is just another coordinate along another axis. In real life we do feel time and dynamics of various processes in a different fashion – time is more like a sequence/collection of snapshots taken at its different moments, in the same sense as a movie being a sequence of frames.
What if we express time in our diagrams in the same way we feel it in the real life – as a sequence of frames in a movie? This way, we would effectively make our two-dimensional plots three-dimensional. How commonly used are actually dynamical visualizations of data in contemporary statistical analysis?
Well, as it turns out, dynamical visualizations are the very cutting edge of presentation technology today. For example, in 2006 statistics guru Hans Rosling has made his famous TED presentation “Debunking myths about the third world” featuring dynamical visualizations of statistical data – if you never saw this video, it is definitely worth checking out – indeed, “you’ve never seen data presented like this”, as he says.
The visualization technology developed and used by Rosling in his TED talk has impressed Google’s bosses so much that the Rosling’s site it was bought by Google in March 2007 to be included into Google Spreadsheets in March 2008 as a standard functionality for data visualization (check out Motion Chart in Google Docs).
To see how good and useful dynamical diagrams can be, you may want to leave NEQNET for the GapMinder website. One of the most interesting diagrams there is “Family size vs. Length of life”, definitely worth watching a couple of times…
Or you may want to stay… Here is another demonstration of dynamical visualization’s power by Sergey Schegloff. What you see on the diagram below is the relation between price and stock’s trading volume for the companies included into Dow Jones Industrial (don’t forget to switch to the log scale!). The latter is a nice illustration of the old brokers’ lore “A rising tide lifts all the boats” (well, actually the very statement goes back to J.F. Kennedy, I believe ): prices of different stocks grow almost homogeneously on a bull market.
Via Sergey Schegloff.
Sunday’s bonus: Really enjoyed reading the discussion (200+ comments) of venture capital income problem on avc.com – one of the most informative ones I’ve ever seen.
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