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Quantum encryption and generalized Shannon impossibility

  • Ching-Yi Lai
  • Kai-Min Chung
Article
  • 21 Downloads

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 \(o(d^{-1})\).

Keywords

Shannon impossibility Information-theoretic security Key length Quantum one-time pad 

Mathematics Subject Classification

94A60 81P94 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Communications EngineeringNational Chiao Tung UniversityHsinchuTaiwan
  2. 2.Institute of Information ScienceAcademia SinicaTaipeiTaiwan

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