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~(4/3(k/(log k))) and memory 2~(2/3(k/(log k))). Using the Dissection technique due to Dinur et al. (Crypto '12) and a novel, slight generalization thereof, we obtain finegrained 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.
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