April 10, 2021

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Lattice Enumeration on GPUs for fplll, by Simon Pohmann and Marc Stevens and Jens Zumbrägel

The Kannan-Fincke-Pohst lattice enumeration algorithm is the classical method for solving the shortest vector problem in lattices. It is also a fundamental tool for most lattice reduction algorithms that provide speed-length tradeoffs. As this algorithm allows efficient parallel implementations, it is likely that implementing it on modern graphics processing units (GPUs) can significantly improve performance. We provide such an implementation that is compatible with the fplll lattice reduction library [fplll16] and achieves a considerable speedup in higher lattice dimensions, compared to current, multithreaded versions. For this, we use the CUDA technology that provides an abstract language for programming GPUs.

[fplll16] The FPLLL development team. “fplll, a lattice reduction library”. 2016. URL: https://github.com/fplll/fplll