Small pseudo-random families of matrices: derandomizing approximate quantum encryption

Andris Ambainis, Adam Smith

Research output: Chapter in Book/Report/Conference proceedingChapter

33 Scopus citations

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 languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsKlaus Jansen, Sanjeev Khanna, Jose D. P. Rolim, Dana Ron
PublisherSpringer Verlag
Pages249-260
Number of pages12
ISBN (Print)3540228942, 9783540228943
DOIs
StatePublished - Jan 1 2004

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3122
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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    Ambainis, A., & Smith, A. (2004). Small pseudo-random families of matrices: derandomizing approximate quantum encryption. In K. Jansen, S. Khanna, J. D. P. Rolim, & D. Ron (Eds.), 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