## Abstract

A Shannon cipher system for memoryless sources in which distortion is allowed at the legitimate decoder is considered. The source is compressed using a secured rate distortion code, which satisfies a constraint on the compression rate, as well as a constraint on the exponential rate of the excess-distortion probability at the legitimate decoder. Secrecy is measured by the exponential rate of the exiguous-distortion probability at the eavesdropper, rather than by the traditional measure of equivocation. The perfect-secrecy exponent is defined as the maximal exiguous-distortion exponent achievable when the key rate is unlimited. The reproduction-based estimate exponent is defined as the maximal exiguous-distortion exponent achievable for a genie-aided eavesdropper, which knows the secret key. Under limited key rate, it is proved that the maximal achievable exiguous-distortion exponent is equal to the minimum between the key rate plus the reproduction-based estimate exponent, and the perfect-secrecy exponent. The result is generalized to a fairly general class of variable key-rate and coding-rate codes.

Original language | English |
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Article number | 7805336 |

Pages (from-to) | 2533-2559 |

Number of pages | 27 |

Journal | IEEE Transactions on Information Theory |

Volume | 63 |

Issue number | 4 |

DOIs | |

State | Published - Apr 2017 |

Externally published | Yes |

## Keywords

- Covering lemmas
- Shannon cipher system
- cryptography
- error exponent
- information-theoretic secrecy
- large-deviations
- lossy compression
- rate-distortion theory
- secret key
- variable-rate codes