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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 9/2019

02-01-2019

Quantum encryption and generalized Shannon impossibility

Authors: Ching-Yi Lai, Kai-Min Chung

Published in: Designs, Codes and Cryptography | Issue 9/2019

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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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Footnotes
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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Metadata
Title
Quantum encryption and generalized Shannon impossibility
Authors
Ching-Yi Lai
Kai-Min Chung
Publication date
02-01-2019
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 9/2019
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-018-00597-3

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