Paper 2018/569

Dissection-BKW

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

Abstract

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 $2^{\frac{4}{3}\frac{k}{\log k}}$ and memory $2^{\frac{2}{3}\frac{k}{\log k}}$. 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.