### Abstract

A quantum encryption scheme (also called private quantum channel, or state randomization protocol) is a one-time pad for quantum messages. If two parties share a classical random string, one of them can transmit a quantum state to the other so that an eavesdropper gets little or no information about the state being transmitted. Perfect encryption schemes leak no information at all about the message. Approximate encryption schemes leak a non-zero (though small) amount of information but require a shorter shared random key. Approximate schemes with short keys have been shown to have a number of applications in quantum cryptography and information theory [8]. This paper provides the first deterministic, polynomial-time constructions of quantum approximate encryption schemes with short keys. Previous constructions [8] are probabilistic - that is, they show that if the operators used for encryption are chosen at random, then with high probability the resulting protocol will be a secure encryption scheme. Moreover, the resulting protocol descriptions are exponentially long. Our protocols use keys of the same length as the probabilistic constructions; to encrypt n qubits approximately, one needs n + o(n) bits of shared key [8], whereas 2n bits of key are necessary for perfect encryption [3]. An additional contribution of this paper is a connection between classical combinatorial derandomization and constructions of pseudo-random matrix families in a continuous space.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Editors | Klaus Jansen, Sanjeev Khanna, Jose D. P. Rolim, Dana Ron |

Publisher | Springer Verlag |

Pages | 249-260 |

Number of pages | 12 |

ISBN (Print) | 3540228942, 9783540228943 |

DOIs | |

State | Published - Jan 1 2004 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3122 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(pp. 249-260). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3122). Springer Verlag. https://doi.org/10.1007/978-3-540-27821-4_23