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Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem

Author Chris Peikert



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Chris Peikert

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Chris Peikert. Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem. In Theoretical Foundations of Practical Information Security. Dagstuhl Seminar Proceedings, Volume 8491, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.08491.4

Abstract

We construct public-key cryptosystems that are secure assuming the *worst-case* hardness of approximating the shortest vector problem on lattices. Prior cryptosystems with worst-case connections (e.g., the Ajtai-Dwork system) were based either on a *special case* of the shortest vector problem, or on the conjectured hardness of lattice problems for *quantum* algorithms. Our main technical innovation is a reduction from certain variants of the shortest vector problem to corresponding versions of the "learning with errors" (LWE) problem; previously, only a quantum reduction of this kind was known. In addition, we construct new cryptosystems based on LWE, including a very natural chosen ciphertext-secure system that has a much simpler description and tighter underlying worst-case approximation factor than prior constructions. (Duration: 30 minutes, on or before Wednesday.)
Keywords
  • Lattice-based cryptography
  • learning with errors
  • quantum computation

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