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The recent decision by the National Institute of Standards and Technology (NIST) to standardize lattice-based cryptography has further increased the demand for security analysis. The Ring-Learning with Error (Ring-LWE) problem is a mathematical problem that constitutes such lattice cryptosystems. It has many algebraic properties because it is considered in the ring of integers, *R*, of a number field, *K*. These algebraic properties make the Ring-LWE based schemes efficient, although some of them are also used for attacks. When the modulus, *q*, is unramified in *K*, it is known that the Ring-LWE problem, to determine the secret information *s* ∈ *R*/*qR*, can be solved by determining *s* (mod q) ∈ **F**_{qf} for all prime ideals q lying over *q*. The χ^{2}-attack determines *s* (mod q) ∈**F*** _{qf}* using chi-square tests over

- Publication
- IEICE TRANSACTIONS on Information Vol.E106-D No.9 pp.1423-1434

- Publication Date
- 2023/09/01

- Publicized
- 2023/07/13

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.2022ICP0017

- Type of Manuscript
- Special Section PAPER (Special Section on Information and Communication System Security)

- Category

Tomoka TAKAHASHI

Osaka University

Shinya OKUMURA

Osaka University

Atsuko MIYAJI

Osaka University

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Tomoka TAKAHASHI, Shinya OKUMURA, Atsuko MIYAJI, "On the Weakness of Non-Dual Ring-LWE Mod Prime Ideal q by Trace Map" in IEICE TRANSACTIONS on Information,
vol. E106-D, no. 9, pp. 1423-1434, September 2023, doi: 10.1587/transinf.2022ICP0017.

Abstract: The recent decision by the National Institute of Standards and Technology (NIST) to standardize lattice-based cryptography has further increased the demand for security analysis. The Ring-Learning with Error (Ring-LWE) problem is a mathematical problem that constitutes such lattice cryptosystems. It has many algebraic properties because it is considered in the ring of integers, *R*, of a number field, *K*. These algebraic properties make the Ring-LWE based schemes efficient, although some of them are also used for attacks. When the modulus, *q*, is unramified in *K*, it is known that the Ring-LWE problem, to determine the secret information *s* ∈ *R*/*qR*, can be solved by determining *s* (mod q) ∈ **F**_{qf} for all prime ideals q lying over *q*. The χ^{2}-attack determines *s* (mod q) ∈**F*** _{qf}* using chi-square tests over

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2022ICP0017/_p

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@ARTICLE{e106-d_9_1423,

author={Tomoka TAKAHASHI, Shinya OKUMURA, Atsuko MIYAJI, },

journal={IEICE TRANSACTIONS on Information},

title={On the Weakness of Non-Dual Ring-LWE Mod Prime Ideal q by Trace Map},

year={2023},

volume={E106-D},

number={9},

pages={1423-1434},

abstract={The recent decision by the National Institute of Standards and Technology (NIST) to standardize lattice-based cryptography has further increased the demand for security analysis. The Ring-Learning with Error (Ring-LWE) problem is a mathematical problem that constitutes such lattice cryptosystems. It has many algebraic properties because it is considered in the ring of integers, *R*, of a number field, *K*. These algebraic properties make the Ring-LWE based schemes efficient, although some of them are also used for attacks. When the modulus, *q*, is unramified in *K*, it is known that the Ring-LWE problem, to determine the secret information *s* ∈ *R*/*qR*, can be solved by determining *s* (mod q) ∈ **F**_{qf} for all prime ideals q lying over *q*. The χ^{2}-attack determines *s* (mod q) ∈**F*** _{qf}* using chi-square tests over

keywords={},

doi={10.1587/transinf.2022ICP0017},

ISSN={1745-1361},

month={September},}

Copy

TY - JOUR

TI - On the Weakness of Non-Dual Ring-LWE Mod Prime Ideal q by Trace Map

T2 - IEICE TRANSACTIONS on Information

SP - 1423

EP - 1434

AU - Tomoka TAKAHASHI

AU - Shinya OKUMURA

AU - Atsuko MIYAJI

PY - 2023

DO - 10.1587/transinf.2022ICP0017

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E106-D

IS - 9

JA - IEICE TRANSACTIONS on Information

Y1 - September 2023

AB - The recent decision by the National Institute of Standards and Technology (NIST) to standardize lattice-based cryptography has further increased the demand for security analysis. The Ring-Learning with Error (Ring-LWE) problem is a mathematical problem that constitutes such lattice cryptosystems. It has many algebraic properties because it is considered in the ring of integers, *R*, of a number field, *K*. These algebraic properties make the Ring-LWE based schemes efficient, although some of them are also used for attacks. When the modulus, *q*, is unramified in *K*, it is known that the Ring-LWE problem, to determine the secret information *s* ∈ *R*/*qR*, can be solved by determining *s* (mod q) ∈ **F**_{qf} for all prime ideals q lying over *q*. The χ^{2}-attack determines *s* (mod q) ∈**F*** _{qf}* using chi-square tests over

ER -