On the complexity of the BKW algorithm on LWE

Abstract : This work presents a study of the complexity of the Blum-Kalai-Wasserman (BKW) algorithm when applied to the Learning with Errors (LWE) problem, by providing re ned estimates for the data and computational e ort requirements for solving concrete instances of the LWE problem. We apply this re ned analysis to suggested parameters for various LWE-based cryptographic schemes from the literature and compare with alternative approaches based on lattice reduction. As a result, we provide new upper bounds for the concrete hardness of these LWE-based schemes. Rather surprisingly, it appears that BKW algorithm outperforms known estimates for lattice reduction algorithms starting in dimension n= 250 when LWE is reduced to SIS. However, this assumes access to an unbounded number of LWE samples.
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Martin Albrecht, Carlos Cid, Jean-Charles Faugère, Robert Fitzpatrick, Ludovic Perret. On the complexity of the BKW algorithm on LWE. Designs, Codes and Cryptography, Springer Verlag, 2015, 74 (2), pp.26. ⟨10.1007/s10623-013-9864-x⟩. ⟨hal-00921517⟩

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