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Erschienen in:
Sieving for Shortest Vectors in Lattices Using Angular Locality-Sensitive Hashing Kapitel lesen Erstes Kapitel lesen

2015 | OriginalPaper | Buchkapitel

Coded-BKW: Solving LWE Using Lattice Codes

verfasst von : Qian Guo, Thomas Johansson, Paul Stankovski

Erschienen in: Advances in Cryptology -- CRYPTO 2015

Verlag: Springer Berlin Heidelberg

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Abstract

In this paper we propose a new algorithm for solving the Learning With Errors (LWE) problem based on the steps of the famous Blum-Kalai-Wasserman (BKW) algorithm. The new idea is to introduce an additional procedure of mapping subvectors into codewords of a lattice code, thereby increasing the amount of positions that can be cancelled in each BKW step. The procedure introduces an additional noise term, but it is shown that by using a sequence of lattice codes with different rates the noise can be kept small. Developed theory shows that the new approach compares favorably to previous methods. It performs particularly well for the binary-LWE case, i.e., when the secret vector is sampled from \(\{0,1\}^*\).

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Vorheriges Kapitel Sieving for Shortest Vectors in Lattices Using Angular Locality-Sensitive Hashing
Nächstes Kapitel An Improved BKW Algorithm for LWE with Applications to Cryptography and Lattices
Fußnoten
1
It is also denoted \(\mathcal {X}_{\sigma }\), and we omit \(\sigma \) if there is no ambiguity.
 
2
Divergence has a couple of aliases in literature: relative entropy, information divergence, Kullback-Leibler divergence, etc. We refer the interested reader to [15] for the rigorous definition. In this paper, the divergence \(\varDelta (\mathcal {X}_{\sigma } \Vert U)\) will be computed numerically.
 
3
The constant factor in the formula is chosen as 4. According to some estimates on linear and differential cryptanalysis (e.g., [6, 33]), its failure probability is fairly low.
 
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Metadaten
Titel
Coded-BKW: Solving LWE Using Lattice Codes
verfasst von
Qian Guo
Thomas Johansson
Paul Stankovski
Copyright-Jahr
2015
Verlag
Springer Berlin Heidelberg
Buch
Advances in Cryptology -- CRYPTO 2015

Print ISBN: 978-3-662-47988-9

Electronic ISBN: 978-3-662-47989-6

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-662-47989-6_2

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