License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.08491.4
URN: urn:nbn:de:0030-drops-18922
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Peikert, Chris

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

08491.PeikertChris.Paper.1892.pdf (0.3 MB)


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.)

BibTeX - Entry

  author =	{Peikert, Chris},
  title =	{{Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem}},
  booktitle =	{Theoretical Foundations of Practical Information Security},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{8491},
  editor =	{Ran Canetti and Shafi Goldwasser and G\"{u}nter M\"{u}ller and Rainer Steinwandt},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-18922},
  doi =		{10.4230/DagSemProc.08491.4},
  annote =	{Keywords: Lattice-based cryptography, learning with errors, quantum computation}

Keywords: Lattice-based cryptography, learning with errors, quantum computation
Collection: 08491 - Theoretical Foundations of Practical Information Security
Issue Date: 2009
Date of publication: 27.02.2009

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