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Computational Security of Quantum Encryption

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Information Theoretic Security (ICITS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10015))

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Abstract

Quantum-mechanical devices have the potential to transform cryptography. Most research in this area has focused either on the information-theoretic advantages of quantum protocols or on the security of classical cryptographic schemes against quantum attacks. In this work, we initiate the study of another relevant topic: the encryption of quantum data in the computational setting. In this direction, we establish quantum versions of several fundamental classical results. First, we develop natural definitions for private-key and public-key encryption schemes for quantum data. We then define notions of semantic security and indistinguishability, and, in analogy with the classical work of Goldwasser and Micali, show that these notions are equivalent. Finally, we construct secure quantum encryption schemes from basic primitives. In particular, we show that quantum-secure one-way functions imply IND-CCA1-secure symmetric-key quantum encryption, and that quantum-secure trapdoor one-way permutations imply semantically-secure public-key quantum encryption.

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Notes

  1. 1.

    While quantum keys might be of interest, they are not necessary for constructing secure schemes [17].

  2. 2.

    Recall that polynomial-time uniformity means that there exists a polynomial-time Turing machine which, on input n in unary, prints a description of the nth circuit in the family.

  3. 3.

    [25] solves the issue by requiring a quantum circuit that takes classical randomness as input and outputs plaintext states. Hence, multiple plaintext states can be generated by using the same randomness.

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Acknowledgements

G. A. was supported by a Sapere Aude grant of the Danish Council for Independent Research, the ERC Starting Grant “QMULT” and the CHIST-ERA project “CQC”. A. B. was supported by Canada’s NSERC. B. F. was supported by the Department of Defense. T. G. was supported by the German Federal Ministry of Education and Research (BMBF) within CRISP and CROSSING. C. S. was supported by a 7th framework EU SIQS and a NWO VIDI grant. M. S. was supported by the Ontario Graduate Scholarship Program. T. G. and C. S. would like to thank COST Action IC1306 for networking support. A. B., G. A., T. G., and C. S. would like to thank the organizers of the Dagstuhl Seminar 15371 “Quantum Cryptanalysis” for providing networking and useful interactions and support during the writing of this paper.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    Gorjan Alagic

  2. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    Anne Broadbent & Michael St. Jules

  3. Joint Center for Quantum Information and Computer Science (QuICS), University of Maryland, College Park, USA

    Bill Fefferman

  4. Cryptoplexity, TU Darmstadt, Darmstadt, Germany

    Tommaso Gagliardoni

  5. QuSoft, University of Amsterdam and CWI, Amsterdam, The Netherlands

    Christian Schaffner

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  1. Gorjan Alagic
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Correspondence to Anne Broadbent or Christian Schaffner .

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Editors and Affiliations

  1. University of Washington Tacoma , Tacoma, Washington, USA

    Anderson C.A. Nascimento

  2. University of Washington , Tacoma, Washington, USA

    Paulo Barreto

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Alagic, G., Broadbent, A., Fefferman, B., Gagliardoni, T., Schaffner, C., St. Jules, M. (2016). Computational Security of Quantum Encryption. In: Nascimento, A., Barreto, P. (eds) Information Theoretic Security. ICITS 2016. Lecture Notes in Computer Science(), vol 10015. Springer, Cham. https://doi.org/10.1007/978-3-319-49175-2_3

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