International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Quantum Lattice Enumeration and Tweaking Discrete Pruning

Yoshinori Aono
Phong Q. Nguyen
Yixin Shen
DOI: 10.1007/978-3-030-03326-2_14
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Presentation: Slides
Conference: ASIACRYPT 2018
Abstract: Enumeration is a fundamental lattice algorithm. We show how to speed up enumeration on a quantum computer, which affects the security estimates of several lattice-based submissions to NIST: if T is the number of operations of enumeration, our quantum enumeration runs in roughly $$\sqrt{T}$$ operations. This applies to the two most efficient forms of enumeration known in the extreme pruning setting: cylinder pruning but also discrete pruning introduced at Eurocrypt ’17. Our results are based on recent quantum tree algorithms by Montanaro and Ambainis-Kokainis. The discrete pruning case requires a crucial tweak: we modify the preprocessing so that the running time can be rigorously proved to be essentially optimal, which was the main open problem in discrete pruning. We also introduce another tweak to solve the more general problem of finding close lattice vectors.
  title={Quantum Lattice Enumeration and Tweaking Discrete Pruning},
  booktitle={Advances in Cryptology – ASIACRYPT 2018},
  series={Lecture Notes in Computer Science},
  author={Yoshinori Aono and Phong Q. Nguyen and Yixin Shen},