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Erschienen in:
Adversary-Dependent Lossy Trapdoor Function from Hardness of Factoring Semi-smooth RSA Subgroup Moduli Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Circular Security Separations for Arbitrary Length Cycles from LWE

verfasst von : Venkata Koppula, Brent Waters

Erschienen in: Advances in Cryptology – CRYPTO 2016

Verlag: Springer Berlin Heidelberg

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Abstract

We describe a public key encryption that is IND-CPA secure under the Learning with Errors (LWE) assumption, but that is not circular secure for arbitrary length cycles. Previous separation results for cycle length greater than 2 require the use of indistinguishability obfuscation, which is not currently realizable under standard assumptions.

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Vorheriges Kapitel Three’s Compromised Too: Circular Insecurity for Any Cycle Length from (Ring-)LWE
Fußnoten
1
For simplicity, we use the notation \(\mathbf{A}^{-1}(\cdot )\) to represent the pre-image \(\mathbf{S}\). In the formal description of our algorithms, we use the pre-image sampling algorithm \(\mathsf {SamplePre}\).
 
2
Applebaum et al. showed that \(\{(\mathbf{A}, \mathbf{s}^{\top }\cdot \mathbf{A} + \mathbf{e}) : \mathbf{A} \leftarrow \mathbb {Z}_q^{n \times m}, \mathbf{s} \leftarrow \chi ^n, \mathbf{e} \leftarrow \chi ^m\}\approx _c \{(\mathbf{A}, \mathbf{u}) : \mathbf{A} \leftarrow \mathbb {Z}_q^{n \times m}, \mathbf{u} \leftarrow \mathbb {Z}_q^m\}\), assuming LWE is hard. However, by a simple hybrid argument, we can replace vectors \(\mathbf{s}, \mathbf{e}, \mathbf{u}\) with matrices \(\mathbf{S}, \mathbf{E}, \mathbf{U}\) of appropriate dimensions.
 
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Metadaten
Titel
Circular Security Separations for Arbitrary Length Cycles from LWE
verfasst von
Venkata Koppula
Brent Waters
Copyright-Jahr
2016
Verlag
Springer Berlin Heidelberg
Buch
Advances in Cryptology – CRYPTO 2016

Print ISBN: 978-3-662-53007-8

Electronic ISBN: 978-3-662-53008-5

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-662-53008-5_24

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