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Massively parallel sharing lattice basis reduction

Please always quote using this URN: urn:nbn:de:0297-zib-85209
under review
  • For cryptanalysis in lattice-based schemes, the performance evaluation of lattice basis reduction using high-performance computers is becoming increasingly important for the determination of the security level. We propose a distributed and asynchronous parallel reduction algorithm based on randomization and DeepBKZ, which is an improved variant of the block Korkine-Zolotarev (BKZ) reduction algorithm. Randomized copies of a lattice basis are distributed to up to 103,680 cores and independently reduced in parallel, while some basis vectors are shared asynchronously among all processes via MPI. There is a trade-off between randomization and information sharing; if a substantial amount of information is shared, all processes will work on the same problem, thereby diminishing the benefit of parallelization. To monitor this balance between randomness and sharing, we propose a metric to quantify the variety of lattice bases. We empirically find an optimal parameter of sharing for high-dimensional lattices. We demonstrate the efficacy of our proposed parallel algorithm and implementation with respect to both performance and scalability through our experiments.

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Metadaten
Author:Nariaki Tateiwa, Yuji ShinanoORCiD, Masaya Yasuda, Shizuo Kaji, Keiichiro Yamamura, Katsuki FujisawaORCiD
Document Type:ZIB-Report
Tag:Discrete optimization; Lattice problem; Lattice-based cryptography; Parallel algorithms; Shortest vector problem; Ubiquity Generator Framework
MSC-Classification:00-XX GENERAL
06-XX ORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES [See also 18B35]
68-XX COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)
CCS-Classification:D. Software
G. Mathematics of Computing
J. Computer Applications
PACS-Classification:00.00.00 GENERAL
Date of first Publication:2021/12/08
Series (Serial Number):ZIB-Report (21-38)
ISSN:1438-0064
Notes:
under review
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