Anzeige
Erschienen in:
2011 | OriginalPaper | Buchkapitel
Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-Decision Reductions
verfasst von : Daniele Micciancio, Petros Mol
Erschienen in: Advances in Cryptology – CRYPTO 2011
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
We study the pseudorandomness of bounded knapsack functions over arbitrary finite abelian groups. Previous works consider only specific families of finite abelian groups and 0-1 coefficients. The main technical contribution of our work is a new, general theorem that provides sufficient conditions under which pseudorandomness of bounded knapsack functions follows directly from their one-wayness. Our results generalize and substantially extend previous work of Impagliazzo and Naor (J. Cryptology 1996).
As an application of the new theorem, we give sample preserving search-to-decision reductions for the Learning With Errors (LWE) problem, introduced by (Regev, STOC 2005) and widely used in lattice-based cryptography. Concretely, we show that, for a wide range of parameters,
m
LWE samples can be proved indistinguishable from random just under the hypothesis that search LWE is a one-way function for the same number
m
of samples.