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Lazy modulus switching for the BKW algorithm on LWE. (English) Zbl 1335.94025
Krawczyk, Hugo (ed.), Public-key cryptography – PKC 2014. 17th international conference on practice and theory in public-key cryptography, Buenos Aires, Argentina, March 26–28, 2014. Proceedings. Berlin: Springer (ISBN 978-3-642-54630-3/pbk). Lecture Notes in Computer Science 8383, 429-445 (2014).
Summary: Some recent constructions based on LWE do not sample the secret uniformly at random but rather from some distribution which produces small entries. The most prominent of these is the binary-LWE problem where the secret vector is sampled from $$\{0,1\}^{ \ast }$$ or $$\{ - 1,0,1\}^{ \ast }$$. We present a variant of the BKW algorithm for binary-LWE and other small secret variants and show that this variant reduces the complexity for solving binary-LWE. We also give estimates for the cost of solving binary-LWE instances in this setting and demonstrate the advantage of this BKW variant over standard BKW and lattice reduction techniques applied to the SIS problem. Our variant can be seen as a combination of the BKW algorithm with a lazy variant of modulus switching which might be of independent interest.
For the entire collection see [Zbl 1283.94002].

##### MSC:
 94A60 Cryptography
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