Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-Decision Reductions
- Daniele MicciancioAffiliated withDepartment of Computer Science & Engineering, University of California
- , Petros MolAffiliated withDepartment of Computer Science & Engineering, University of California
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.
- Pseudorandom Knapsacks and the Sample Complexity of LWE Search-to-Decision Reductions
- Book Title
- Advances in Cryptology – CRYPTO 2011
- Book Subtitle
- 31st Annual Cryptology Conference, Santa Barbara, CA, USA, August 14-18, 2011. Proceedings
- pp 465-484
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- International Association for Cryptologic Research
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