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Paper 2008/481

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

Chris Peikert

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.

Metadata
Available format(s)
PDF PS
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Lattice-based cryptographylearning with errorsquantum computation
Contact author(s)
cpeikert @ alum mit edu
History
2008-11-19: received
Short URL
https://ia.cr/2008/481
License
Creative Commons Attribution
CC BY
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