Paper 2018/546
Quantum Lattice Enumeration and Tweaking Discrete Pruning
Yoshinori Aono, Phong Q. Nguyen, and Yixin Shen
Abstract
Enumeration is a fundamental lattice algorithm used in challenge records. 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.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- A major revision of an IACR publication in ASIACRYPT 2018
- Keywords
- LatticesQuantum algorithmsEnumeration
- Contact author(s)
- Phong Nguyen @ inria fr
- History
- 2018-09-07: revised
- 2018-06-04: received
- See all versions
- Short URL
- https://ia.cr/2018/546
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2018/546,
author = {Yoshinori Aono and Phong Q. Nguyen and Yixin Shen},
title = {Quantum Lattice Enumeration and Tweaking Discrete Pruning},
howpublished = {Cryptology {ePrint} Archive, Paper 2018/546},
year = {2018},
url = {https://eprint.iacr.org/2018/546}
}
