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

  • Daniele Micciancio
  • Petros Mol
Conference paper

DOI: 10.1007/978-3-642-22792-9_26

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6841)
Cite this paper as:
Micciancio D., Mol P. (2011) Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-Decision Reductions. In: Rogaway P. (eds) Advances in Cryptology – CRYPTO 2011. CRYPTO 2011. Lecture Notes in Computer Science, vol 6841. Springer, Berlin, Heidelberg


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.

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Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Daniele Micciancio
    • 1
  • Petros Mol
    • 1
  1. 1.Department of Computer Science & EngineeringUniversity of CaliforniaSan DiegoUSA

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