International Association for Cryptologic Research

International Association
for Cryptologic Research


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

Chris Peikert
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Abstract: We construct public-key cryptosystems that are secure assuming the \emph{worst-case} hardness of approximating the length of a shortest nonzero vector in an $n$-dimensional lattice to within a small $\poly(n)$ factor. Prior cryptosystems with worst-case connections were based either on the shortest vector problem for a \emph{special class} of lattices (Ajtai and Dwork, STOC 1997; Regev, J.~ACM 2004), or on the conjectured hardness of lattice problems for \emph{quantum} algorithms (Regev, STOC 2005). 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 \emph{quantum} reduction of this kind was known. In addition, we construct new cryptosystems based on the \emph{search} version of $\lwe$, including a very natural \emph{chosen ciphertext-secure} system that has a much simpler description and tighter underlying worst-case approximation factor than prior constructions.
  title={Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem},
  booktitle={IACR Eprint archive},
  keywords={foundations / Lattice-based cryptography, learning with errors, quantum computation},
  note={ 14197 received 13 Nov 2008},
  author={Chris Peikert},