Rank-2 module-LIP with special matrices

Manoj Gyawali

doi:10.1016/j.ipl.2025.106593

Rank-2 module-LIP with special matrices

Manoj Gyawali

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Lattice isomorphism problem (LIP) has been studied since 1990s. In 2023, a post-quantum signature scheme known as HAWK was submitted in the NIST standardization of additional signature scheme, which is based on the module lattice isomorphism problem (module-LIP). Module-LIP was formally defined by Mureau et al. at Eurocrypt'24 and Luo et al. reduced the problem of solving module-LIP over CM number fields to a problem of finding the special type of symplectic automorphism. In this paper, we extend this idea further by establishing a reduction of the module-LIP to a problem of finding special types of matrices.

Original language	English
Article number	106593
Journal	Information Processing Letters
Volume	191
DOIs	https://doi.org/10.1016/j.ipl.2025.106593
Publication status	Published - Jan 2026

Keywords

CM-order
HAWK
Module lattice
Module-LIP
Reduction of a problem

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abstract = "Lattice isomorphism problem (LIP) has been studied since 1990s. In 2023, a post-quantum signature scheme known as HAWK was submitted in the NIST standardization of additional signature scheme, which is based on the module lattice isomorphism problem (module-LIP). Module-LIP was formally defined by Mureau et al. at Eurocrypt'24 and Luo et al. reduced the problem of solving module-LIP over CM number fields to a problem of finding the special type of symplectic automorphism. In this paper, we extend this idea further by establishing a reduction of the module-LIP to a problem of finding special types of matrices.",

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N2 - Lattice isomorphism problem (LIP) has been studied since 1990s. In 2023, a post-quantum signature scheme known as HAWK was submitted in the NIST standardization of additional signature scheme, which is based on the module lattice isomorphism problem (module-LIP). Module-LIP was formally defined by Mureau et al. at Eurocrypt'24 and Luo et al. reduced the problem of solving module-LIP over CM number fields to a problem of finding the special type of symplectic automorphism. In this paper, we extend this idea further by establishing a reduction of the module-LIP to a problem of finding special types of matrices.

AB - Lattice isomorphism problem (LIP) has been studied since 1990s. In 2023, a post-quantum signature scheme known as HAWK was submitted in the NIST standardization of additional signature scheme, which is based on the module lattice isomorphism problem (module-LIP). Module-LIP was formally defined by Mureau et al. at Eurocrypt'24 and Luo et al. reduced the problem of solving module-LIP over CM number fields to a problem of finding the special type of symplectic automorphism. In this paper, we extend this idea further by establishing a reduction of the module-LIP to a problem of finding special types of matrices.

KW - CM-order

KW - HAWK

KW - Module lattice

KW - Module-LIP

KW - Reduction of a problem

UR - https://www.scopus.com/pages/publications/105007724469

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DO - 10.1016/j.ipl.2025.106593

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SN - 0020-0190

VL - 191

JO - Information Processing Letters

JF - Information Processing Letters

M1 - 106593

ER -

Rank-2 module-LIP with special matrices

Abstract

Keywords

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