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

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 tradeoffs. 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 2 and space 2, improving upon the previous best triple sieve time complexity of 2 of Herold–Kirshanova. Using more memory we obtain better asymptotic time complexities. For instance, we obtain a triple sieve requiring only 2 time and 2 memory to solve SVP in dimension n. This improves upon the best double Gauss sieve of Becker–Ducas–Gama–Laarhoven, which runs in 2 time when using the same amount of space.