## Cryptology ePrint Archive: Report 2018/546

Quantum Lattice Enumeration and Tweaking Discrete Pruning

Yoshinori Aono and 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.

Category / Keywords: public-key cryptography / Lattices, Quantum algorithms, Enumeration

Original Publication (with major differences): IACR-ASIACRYPT-2018

Date: received 2 Jun 2018, last revised 7 Sep 2018

Contact author: Phong Nguyen at inria fr

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2018/546

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