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Quantum encryption and generalized Shannon impossibility

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Abstract

The famous Shannon impossibility result says that any encryption scheme with perfect secrecy requires a secret key at least as long as the message. In this paper we provide its quantum analogue with imperfect secrecy and imperfect correctness. We also give a systematic study of information-theoretically secure quantum encryption with two secrecy definitions. We show that the weaker one implies the stronger but with a security loss in d, where d is the dimension of the encrypted quantum system. This is good enough if the target secrecy error is of \(o(d^{-1})\).

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Notes

  1. Note that the righthand side of Eq. (41) in [5] should be \((1-\epsilon )^2\) and hence there should be an additional factor of 2 in front of the term \(\log (1-\epsilon )\) in the lower bound.

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Acknowledgements

We are grateful to anonymous referees for their constructive comments on this manuscript. CYL was was financially supported from the Young Scholar Fellowship Program by Ministry of Science and Technology (MOST) in Taiwan, under Grant MOST107-2636-E-009-005. KMC was partially supported by 2016 Academia Sinica Career Development Award under Grant No. 23-17 and the Ministry of Science and Technology, Taiwan under Grant No. MOST 103-2221-E-001-022-MY3.

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Authors and Affiliations

  1. Institute of Communications Engineering, National Chiao Tung University, Hsinchu, 30010, Taiwan

    Ching-Yi Lai

  2. Institute of Information Science, Academia Sinica, No 128, Academia Road, Section 2, Nankang, Taipei, 11529, Taiwan

    Kai-Min Chung

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  1. Ching-Yi Lai
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  2. Kai-Min Chung
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Correspondence to Ching-Yi Lai.

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Communicated by A. Winterhof.

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Lai, CY., Chung, KM. Quantum encryption and generalized Shannon impossibility. Des. Codes Cryptogr. 87, 1961–1972 (2019). https://doi.org/10.1007/s10623-018-00597-3

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