Speed-ups and time-memory trade-offs for tuple lattice sieving

摘要: In this work we study speed-ups and time–space trade-offs for solving the shortest vector problem (SVP) on Euclidean lattices based on tuple lattice sieving. Our results extend and improve upon previous work of Bai–Laarhoven–Stehlé [ANTS’16] and Herold–Kirshanova [PKC’17], with better complexities for arbitrary tuple sizes and offering tunable time–memory trade-offs. The trade-offs we obtain stem from the generalization and combination of two algorithmic techniques: the configuration framework introduced by Herold–Kirshanova, and the spherical locality-sensitive filters of Becker–Ducas–Gama–Laarhoven [SODA’16]. When the available memory scales quasi-linearly with the list size, we show that with triple sieving we can solve SVP in dimension n in time and space , improving upon the previous best triple sieve time complexity of of Herold–Kirshanova. Using …