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The Module Lattice Isomorphism Problem (Module-LIP) is one of the lattice building blocks of the post-quantum cryptographic schemes, in particular HAWK signature scheme. In 2024, Mureau et al. introduced an algorithm to solve the lattice isomorphism problem of rank 2 Module-lattices over a totally real number field. In this paper, we revisit this algorithm and suggest an improvement making the algorithm more than 40% faster and we give some perspectives for future cryptanalysis works. As an application, we propose a partial-key exposure attack and demonstrate the impact of our study on exploiting side-information from leaks on the HAWK signature scheme.

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An Improvement of the Congruence Solver of Lattice Isomorphism Problem over Totally Real Number Fields and Applications

  • 会议论文

  • 发表日期：

    2026年

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  • Nour-eddine Rahmani,
  • Taoufik Serraj,
  • Moulay Chrif Ismaili

摘要

The Module Lattice Isomorphism Problem (Module-LIP) is one of the lattice building blocks of the post-quantum cryptographic schemes, in particular HAWK signature scheme. In 2024, Mureau et al. introduced an algorithm to solve the lattice isomorphism problem of rank 2 Module-lattices over a totally real number field. In this paper, we revisit this algorithm and suggest an improvement making the algorithm more than 40% faster and we give some perspectives for future cryptanalysis works. As an application, we propose a partial-key exposure attack and demonstrate the impact of our study on exploiting side-information from leaks on the HAWK signature scheme.