@inproceedings{33326fb8c4fb4bf3b659b22aa06ee5e9,

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

abstract = "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.",

keywords = "Closest vector problem (CVP), Lattice enumeration, Lattice sieving, Randomized slicer, Shortest vector problem (SVP)",

author = "Emmanouil Doulgerakis and Thijs Laarhoven and {de Weger}, Benne",

year = "2020",

doi = "10.1007/978-3-030-51938-4_15",

language = "English",

isbn = "9783030519377",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Gabler",

pages = "301--320",

editor = "Abderrahmane Nitaj and Amr Youssef",

booktitle = "Progress in Cryptology - AFRICACRYPT 2020 - 12th International Conference on Cryptology in Africa, Proceedings",

address = "Germany",

note = "12th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2020 ; Conference date: 20-07-2020 Through 22-07-2020",

}