Paper 2021/1295

Improved Quantum Hypercone Locality Sensitive Filtering in Lattice Sieving

Max Heiser


The asymptotically fastest known method for solving SVP is via lattice sieving, an algorithm whose computational bottleneck is solving the Nearest Neighbor Search problem. The best known algorithm for solving this problem is Hypercone Locality Sensitive Filtering (LSF). The classical time complexity of a sieve using Hypercone LSF is \(2^{0.2925d+o(d)}\). The quantum time complexity is \(2^{0.2653d+o(d)}\), which is acquired by using Grover's algorithm to speed up part of the enumeration. We present an improvement to the quantum algorithm, which improves the time complexity to \(2^{0.2571d+o(d)}\). Essentially, we provide a way to use Grover's algorithm to speed up another part of the process, providing a better tradeoff. This improvement affects the security of lattice-based encryption schemes, including NIST PQC Round 3 finalists.

Available format(s)
Public-key cryptography
Publication info
Preprint. Minor revision.
lattice-based cryptographySVPsieving algorithmscryptanalysislattice techniques
Contact author(s)
heisermax @ protonmail com
2021-09-27: received
Short URL
Creative Commons Attribution


      author = {Max Heiser},
      title = {Improved Quantum Hypercone Locality Sensitive Filtering in Lattice Sieving},
      howpublished = {Cryptology ePrint Archive, Paper 2021/1295},
      year = {2021},
      note = {\url{}},
      url = {}
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