### Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-Decision Reductions

Daniele Micciancio and Petros Mol

##### Abstract

We study under what conditions the conjectured one-wayness of the knapsack function (with polynomially bounded inputs) over an arbitrary finite abelian group implies that the output of the function is pseudorandom, i.e., computationally indistinguishable from a uniformly chosen group element. Previous work of Impagliazzo and Naor (J. Cryptology 9(4):199-216, 1996) considers only specific families of finite abelian groups and uniformly chosen random \emph{binary} inputs. Our work substantially extends previous results and provides a much more general reduction that applies to arbitrary finite abelian groups and input distributions with polynomially bounded coefficients. As an application of the new result, we give \emph{sample preserving} search-to-decision reductions for the Learning With Errors (LWE) problem, introduced by Regev (J. ACM 56(6):34, 2009) and widely used in lattice-based cryptography.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. A preliminary version of this work appears in the Proceedings of CRYPTO 2011. This is the full version of the paper.
Contact author(s)
pmol @ cs ucsd edu
History
2011-09-26: last of 2 revisions
See all versions
Short URL
https://ia.cr/2011/521

CC BY

BibTeX

@misc{cryptoeprint:2011/521,
author = {Daniele Micciancio and Petros Mol},
title = {Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-Decision Reductions},
howpublished = {Cryptology ePrint Archive, Paper 2011/521},
year = {2011},
note = {\url{https://eprint.iacr.org/2011/521}},
url = {https://eprint.iacr.org/2011/521}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.