New infinity-norm method speeds rank-2 lattice reduction
Original title: Fast \(\ell_\infty\)-Reduction of Rank-2 Lattices in $\mathbb{R}^n$ via a New Reduced-Basis Notion
The algorithm matches Lagrange-Gauss complexity at O(nT^2) and saves at least 2n multiplications per iteration.
Researchers introduce a reduced-basis notion and an algorithm for rank-two lattices under the infinity norm, motivated by lattice cryptography and ML-DSA security analysis. Each non-terminal iteration guarantees a factor-two drop in the maximum infinity norm of the basis vectors. They prove termination and a bit complexity of O(nT^2), matching classical Lagrange-Gauss order, while saving at least 2n multiplications per iteration. Experiments show runtime gains, especially on high-dimensional lattices.
- The method uses a dominant coordinate for a multi-dimensional analogue of Euclidean division.
- Each non-terminal step halves the maximum infinity norm of the basis.
- The paper positions the result as a foundation for infinity-norm reduction.
From the original article
1 min read at arxiv.orgThe shortest vector problem (SVP) under the infinity norm ($\ell_\infty$-norm) is an important lattice problem with applications in lattice-based cryptography. In particular, the security analysis of the post-quantum signature standard ML-DSA highlights the importance of finding short solutions satisfying infinity-norm constraints, rather than only Euclidean norm bounds.
By Bo Pang · arxiv.org
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