Abstract
Regarding the security concerns arising from the threat that quantum computing algorithms pose on some today’s most efficient and widely implemented public-key cryptographic systems, it has become necessary to find alternative cryptographic techniques to support private (or symmetric) key cryptographic schemes by means of key distribution. In this article we survey the emerging technology of quantum key distribution (QKD), which enables two separate parties to distill a random secret key only known by them and whose security relies on the principles of quantum physics, with the advantage of also enabling the detection of potential eavesdroppers. Among the different existing approaches to QKD, a distinction is made between discrete and continuous variable protocols. We focus here on continuous variable (CV-QKD) protocols, which consist of encoding information in optical coherent states that can be transmitted by fiber by means of off-the-shelf devices widely used in today’s telecommunications industry. An important advantage is that these components have a significantly lower cost in comparison to those used in other QKD protocols. The present study highlights some information-theoretic aspects of CV-QKD while putting special efforts into the security analysis of these protocols (such as parameter estimation or error correction techniques) derived from the practical implementation, as well as the challenges this technology faces in its still ongoing development.
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Notes
- 1.
There are two variants of protocols for the preparation, transmission and measurement of states, PM (Prepare-and-Measure) and E-B (Entanglement-Based). Both are indistinguishable from the point of view of Bob and Eve, and equivalent concerning the security analysis. The second one, however, is more difficult to implement while the analysis of the first is more cumbersome, which therefore makes it convenient to benefit from their equivalences to simplify both the implementation and the analysis; the protocol is implemented in the PM version while the security analysis is performed considering a virtualization of the equivalent E-B protocol.
- 2.
It should be noted that, in the practical implementation, the protocol is initialized assuming typical experimental values -i.e. reasonable guesses- of T and \(\xi \) and the chosen value for the variance will be that which maximizes the a priori expected secret key rate. The real values will be estimated after transmission during the PE phase and the bounds on the secret key rate adjusted.
- 3.
Classes of attacks will be highlighted in the following section.
- 4.
Since standard telecommunications systems widely implement discrete constellations with 64, 128 and 256 states.
- 5.
As a result of the quantum nature of the exchanged states.
- 6.
For the reader unfamiliar with this notation, in the quantum formalism the Greek letter \(\rho \) is used to denote the density matrix -or density operator- that represents all the possibly available information about the state of a quantum object.
- 7.
\(\frac{\partial S(B;E)}{\partial t } < 0 \) y \(\frac{\partial S(B;E)}{\partial \sigma ^2 } > 0\).
- 8.
Explicit expressions for the three eigenvalues are known and can be found in [7].
- 9.
A typical value for the true excess noise can be \(\varDelta _{\textrm{m}} \xi = 1/100\). Similarly, it is often chosen \(\epsilon = \epsilon _{\textrm{PE}} = 10^{-10}\) and therefore \(z_{\epsilon _{\textrm{PE}}/2} \approx 6.5\).
- 10.
For example, the amount m of samples required to transmit a secret key rate over 100 km would be of the order of \(10^{10}\) [7].
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Acknowledgements
This work had the support of Grant PID2020-118178RB-C22 funded by AEI/10.13039/501100011033, and by the Community of Madrid (Spain) under the CYNAMON project (P2018/TCS-4566), co-financed with European Social Fund and EU FEDER funds. We also acknowledge the support of the Spanish National Research Council (CSIC), project 202050E232, and CSIC’s Interdisciplinary Thematic Platform (PTI+) on Quantum Technologies (PTI-QTEP+). This study was supported by CSIC’s program for the Spanish Recovery, Transformation and Resilience Plan funded by the Recovery and Resilience Facility of the European Union, established by the Regulation (EU) 2020/2094; and MCIN with funding from European Union NextGenerationEU (PRTR-C17.I1).
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Garcia-Callejo, A., Ruiz-Chamorro, A., Cano, D., Fernandez, V. (2023). A Review on Continuous-Variable Quantum Key Distribution Security. In: Bravo, J., Ochoa, S., Favela, J. (eds) Proceedings of the International Conference on Ubiquitous Computing & Ambient Intelligence (UCAmI 2022). UCAmI 2022. Lecture Notes in Networks and Systems, vol 594. Springer, Cham. https://doi.org/10.1007/978-3-031-21333-5_107
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