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Self-dual DeepBKZ for finding short lattice vectors. (English) Zbl 1448.94235
Summary: In recent years, the block Korkine-Zolotarev (BKZ) and its variants such as BKZ 2.0 have been used as de facto algorithms to estimate the security of a lattice-based cryptosystem. In 2017 [the author et al., NuTMiC 2017, Lect. Notes Comput. Sci. 10737, 142–160 (2018; Zbl 1423.94115)], DeepBKZ was proposed as a mathematical improvement of BKZ, which calls LLL with deep insertions (DeepLLL) as a subroutine alternative to LLL. DeepBKZ can find a short lattice vector by smaller blocksizes than BKZ. In this paper, we develop a self-dual variant of DeepBKZ, as in the work of D. Micciancio and M. Walter [Eurocrypt 2016, Lect. Notes Comput. Sci. 9665, 820–849 (2016; Zbl 1385.94062)] for self-dual BKZ. Like DeepBKZ, our self-dual DeepBKZ calls both DeepLLL and its dual variant as main subroutines in order to accelerate to find a very short lattice vector. We also report experimental results of DeepBKZ and our self-dual DeepBKZ for random bases on the Darmstadt SVP challenge.

MSC:
94A60 Cryptography
68P25 Data encryption (aspects in computer science)
68W30 Symbolic computation and algebraic computation
Software:
BKZ; fpLLL; GitHub; NTL
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References:
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