Paper 2018/569


Andre Esser, Felix Heuer, Robert Kübler, Alexander May, and Christian Sohler


The slightly subexponential algorithm of Blum, Kalai and Wasserman (BKW) provides a basis for assessing LPN/LWE security. However, its huge memory consumption strongly limits its practical applicability, thereby preventing precise security estimates for cryptographic LPN/LWE instantiations. We provide the first time-memory trade-offs for the BKW algorithm. For instance, we show how to solve LPN in dimension $k$ in time $2^{\frac 43\frac k{\log k}}$ and memory $2^{\frac 23\frac k{\log k}}$. Using the Dissection technique due to Dinur et al. (Crypto ’12) and a novel, slight generalization thereof, we obtain fine-grained trade-offs for any available (subexponential) memory while the running time remains subexponential. Reducing the memory consumption of BKW below its running time also allows us to propose a first quantum version QBKW for the BKW algorithm.

Available format(s)
Publication info
A major revision of an IACR publication in CRYPTO 2018
CryptanalysisLPNBKW algorithmDissectionTime-Memory Trade-Off
Contact author(s)
andre esser @ rub de
2018-06-05: received
Short URL
Creative Commons Attribution


      author = {Andre Esser and Felix Heuer and Robert Kübler and Alexander May and Christian Sohler},
      title = {Dissection-BKW},
      howpublished = {Cryptology ePrint Archive, Paper 2018/569},
      year = {2018},
      note = {\url{}},
      url = {}
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