Finished project

Quantum information theory, esp. Quantum cryptography

PhD student: Aishajiang Abuding
Supervisor: Jan-Åke Larsson (MAI)
Co-supervisor: Viiveke Fåk (ISY)

The research is about similarities and differences between our common everyday concepts and the concepts used within Quantum Mechanics. In our usual (classical) world, objects have objective properties like position and speed. In Quantum Mechanics, an object is instead described by its wave function, which does not specify the position or the speed. In fact, the object is not said to have position or speed until one of them is measured. In addition, one cannot measure position and speed at the same time with high accuracy, and the usual conclusion is that a quantum object cannot have both the properties of position and speed at the same time (these two properties are said to be complementary).

There are a number of recent applications that use this to, for example, factorize large numbers quickly ("Shor's algorithm") or do fast searches in an unsorted database ("Grover's algorithm"). Another application is Quantum Cryptography, where the basis of security is precisely the mentioned complementarity (of, e.g., position and speed), and the data protection stems from the so-called Einstein- Podolsky-Rosen-paradox. In one of the existing implementations, the protection is based on "Bell's inequality" (closely examined in Jan-Åke's PhD thesis). This area of research is called Quantum Information Theory.

Jan-Åke has published a number of papers in Quantum Cryptography, for example on whether one really can tell the difference between a quantum-mechanical implementation and a classical implementation that "pretends" to be quantum. The question is important because if one cannot tell the difference, it is possible for the manufacturer to include a built-in Trojan horse in the system. Another example concerns a protocol published in 2004 where a problem was identified. The proposed security test was not enough to guarantee security, but in Jan-Åke's paper there is an improvement that results in a secure protocol.

The latest analysis (together with the Master's student Jörgen Cederlöf) concerns the classical protocol needed in every quantum cryptography system for secure key production. Especially, one necessary component: cryptographically secure authentication. The study has shown that the current protocols need to be changed ("patched") since they can be insecure in their present form. Some properties of the authentication still needs to be examined more closely. It is also possible to examine other protocols, also those that do not describe key generation/transfer, for example other cryptographical tasks or pure communication protocols. There are a plethora of suggestions of this kind since the technology is rapidly becoming commerciably available.

We plan to make use of the existing cryptographic competence at the department of Electrical Engineering, but we also note that a preliminary study on Quantum Cryptography has been started at the Swedish Defense Research Institute (FOI). Being only preliminary, the study concentrates on choosing appropriate physical components rather than examining theoretical background. Nonetheless, the need for theoretical expertise is to be expected, and establishing this competence at the university opens up the possibilities for a future cooperation with FOI.

Publications

Licentiate dissertation

Aysajan Abidin, Weaknesses of Authentication inQuantum Cryptography and Strongly Universal Hash Functions (2010)

Articles

Abidin, Aysajan; Larsson, Jan-Åke, Vulnerability of "A Novel Protocol-Authentication Algorithm Ruling out a Man-in-the-Middle Attack in Quantum Cryptography" (2009)

Conference Papers

Abidin, Aysajan; Larsson, Jan-Åke, Special Properties of Strongly Universal2 Hash Functions Important in Quantum Cryptography (2009)

References

Security aspects of the Authentication used in Quantum Cryptography, Jörgen Cederlöf and Jan-Åke Larsson, Foundations of Probability and Physics-4, 4 - 9 juni 2006, Växjö Universitet, Växjö, http://arxiv.org/abs/quant-ph/0611009. No information flow using statistical fluctuations and quantum cryptography, Jan- Åke Larsson, Phys. Rev. A, 69:042317 (2004), also chosen for the May issue 2004 of the Virtual Journal of Quantum Information, http://arxiv.org/abs/quant-ph/0308107. A practical Trojan Horse for Bell-inequality-based quantum cryptography, Jan- Åke Larsson, Quantum Information and Computation, 2:434 (2002), http://arxiv.org/abs/quant-ph/0111073.

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Last updated: 2011-06-07