… sieving algorithms to solve SVP with less memory. We consider reductions of tuples of vectors
rather than pairs of vectors as existing sieve … The naive algorithm for this triple sieve runs …

… It serves as a useful abstraction of the tuple lattice sieving problem for which our results
are provable – the results only become heuristic when applying them to tuple lattice sieving. …

… their results for arbitrary tuple sizes, for example showing that a triple sieve can solve the …
to tuple lattice sieving to obtain even better time complexities. For instance, our triple sieve …

… progressive approach to lattice sieving, where we gradually introduce new basis vectors only
when the sieve has stabilized … For tuple sieving [BLS16, HK17, HKL18] we simply run tuple …

… In this work, we report performance records for achieving various lattice reduction tasks
using sieving. For exact-SVP, we are able to outperform the pruned enumeration of FPLLL/…

… After the sieving part we have a list of tuples with indices and the corresponding length of
the new vector they represent. The hash identifier of the new vector can efficiently be …

… of sieve-type algorithms. Precisely, we show that a few calls to the sieve algorithm in lattices
… applied to most other variants of sieve algorithms, including LSH sieve algorithms and tuple-…

… of lattice problems based on the sieving technique due to … M ⊆ Rn and a full rank integer
lattice L ⊆ Qn, the subspace … }, T ⊂ [N] be the set of tuples left after the sieving procedure. …

… preliminaries on lattice and sieve algorithms. Section III provides an overview of sieve algorithms
… Moreover, by applying tuple sieve technique to Gauss Sieve algorithm, they proposed …

… , MO15], and especially in lattice sieving many subsequent … For the applications of interest
in this paper (lattice sieving … Similar optimality results extend to the tuple sieving results of …