### Quantum Augmented Dual Attack

##### Abstract

We present a quantum augmented variant of the dual lattice attack on the Learning with Errors (LWE) problem, using classical memory with quantum random access (QRACM). Applying our results to lattice parameters from the literature, we find that our algorithm outperforms previous algorithms, assuming unit cost access to a QRACM. On a technical level, we show how to obtain a quantum speedup on the search for Fast Fourier Transform (FFT) coefficients above a given threshold by leveraging the relative sparseness of the FFT and using quantum amplitude estimation. We also discuss the applicability of the Quantum Fourier Transform in this context. Furthermore, we give a more rigorous analysis of the classical and quantum expected complexity of guessing part of the secret vector where coefficients follow a discrete Gaussian (mod $$q$$).

Available format(s)
Category
Attacks and cryptanalysis
Publication info
Preprint.
Keywords
Learning with Errors Dual attack Fast Fourier Transform Quantum algorithms Amplitude Estimation
Contact author(s)
martin albrecht @ rhul ac uk
yixin shen @ rhul ac uk
History
2022-05-31: approved
See all versions
Short URL
https://ia.cr/2022/656

CC BY

BibTeX

@misc{cryptoeprint:2022/656,
author = {Martin R. Albrecht and Yixin Shen},
title = {Quantum Augmented Dual Attack},
howpublished = {Cryptology ePrint Archive, Paper 2022/656},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/656}},
url = {https://eprint.iacr.org/2022/656}
}

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