Sieve, enumerate, slice, and lift:: Hybrid lattice algorithms for svp via cvpp

Samenvatting

Motivated by recent results on solving large batches of closest vector problem (CVP) instances, we study how these techniques can be combined with lattice enumeration to obtain faster methods for solving the shortest vector problem (SVP) on high-dimensional lattices. Theoretically, under common heuristic assumptions we show how to solve SVP in dimension d with a cost proportional to running a sieve in dimension $$d - \varTheta (d / \log d)$$, resulting in a $$2^{\varTheta (d / \log d)}$$ speedup and memory reduction compared to running a full sieve. Combined with techniques from [Ducas, Eurocrypt 2018] we can asymptotically get a total of $$[\log (13/9) + o(1)] \cdot d / \log d$$ dimensions for free for solving SVP. Practically, the main obstacles for observing a speedup in moderate dimensions appear to be that the leading constant in the $$\varTheta (d / \log d)$$ term is rather small; that the overhead of the (batched) slicer may be large; and that competitive enumeration algorithms heavily rely on aggressive pruning techniques, which appear to be incompatible with our algorithms. These obstacles prevented this asymptotic speedup (compared to full sieving) from being observed in our experiments. However, it could be expected to become visible once optimized CVPP techniques are used in higher dimensional experiments.

Originele taal-2 Engels Progress in Cryptology - AFRICACRYPT 2020 - 12th International Conference on Cryptology in Africa, Proceedings Abderrahmane Nitaj, Amr Youssef Springer Gabler 301-320 20 9783030519377 https://doi.org/10.1007/978-3-030-51938-4_15 Gepubliceerd - 2020 12th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2020 - Cairo, EgypteDuur: 20 jul 2020 → 22 jul 2020

Publicatie series

Naam Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 12174 LNCS 0302-9743 1611-3349

Congres

Congres 12th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2020 Egypte Cairo 20/07/20 → 22/07/20