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On the Use of Quantum Entanglement in Secure Communications: A Survey

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 Added by Ozan Tonguz K.
 Publication date 2020
and research's language is English




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Quantum computing and quantum communications are exciting new frontiers in computing and communications. Indeed, the massive investments made by the governments of the US, China, and EU in these new technologies are not a secret and are based on the expected potential of these technologies to revolutionize communications, computing, and security. In addition to several field trials and hero experiments, a number of companies such as Google and IBM are actively working in these areas and some have already reported impressive demonstrations in the past few years. While there is some skepticism about whether quantum cryptography will eventually replace classical cryptography, the advent of quantum computing could necessitate the use of quantum cryptography as the ultimate frontier of secure communications. This is because, with the amazing speeds demonstrated with quantum computers, breaking cryptographic keys might no longer be a daunting task in the next decade or so. Hence, quantum cryptography as the ultimate frontier in secure communications might not be such a far-fetched idea. It is well known that Heisenbergs Uncertainty Principle is essentially a negative result in Physics and Quantum Mechanics. It turns out that Heisenbergs Uncertainty Principle, one of the most interesting results in Quantum Mechanics, could be the theoretical basis and the main scientific principle behind the ultimate frontier in quantum cryptography or secure communications in conjunction with Quantum Entanglement.



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We construct several explicit quantum secure non-malleable-extractors. All the quantum secure non-malleable-extractors we construct are based on the constructions by Chattopadhyay, Goyal and Li [2015] and Cohen [2015]. 1) We construct the first explicit quantum secure non-malleable-extractor for (source) min-entropy $k geq textsf{poly}left(log left( frac{n}{epsilon} right)right)$ ($n$ is the length of the source and $epsilon$ is the error parameter). Previously Aggarwal, Chung, Lin, and Vidick [2019] have shown that the inner-product based non-malleable-extractor proposed by Li [2012] is quantum secure, however it required linear (in $n$) min-entropy and seed length. Using the connection between non-malleable-extractors and privacy amplification (established first in the quantum setting by Cohen and Vidick [2017]), we get a $2$-round privacy amplification protocol that is secure against active quantum adversaries with communication $textsf{poly}left(log left( frac{n}{epsilon} right)right)$, exponentially improving upon the linear communication required by the protocol due to [2019]. 2) We construct an explicit quantum secure $2$-source non-malleable-extractor for min-entropy $k geq n- n^{Omega(1)}$, with an output of size $n^{Omega(1)}$ and error $2^{- n^{Omega(1)}}$. 3) We also study their natural extensions when the tampering of the inputs is performed $t$-times. We construct explicit quantum secure $t$-non-malleable-extractors for both seeded ($t=d^{Omega(1)}$) as well as $2$-source case ($t=n^{Omega(1)}$).
This is a report and a collection of abstracts from the Feb. 2008 Lausanne Workshop on Secure Vehicular Communication Systems.
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