Ming Luo

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cs.CR2026

Module Lattice Security (Part II): Module Lattice Reduction via Optimal Sign Selection

Ming-Xing Luo

We extend the CDPR's quantum attack from ideal lattices to module lattices over $2^{k}$ -th cyclotomic rings. Using trace orthogonality of the power basis, we decompose a rank- $d$ mod…

cs.CR2026

Module Lattice Security (Part I): Unconditional Verification of Weber's Conjecture for $k \leq 12$

Ming-Xing Luo

Weber's conjecture (1886) governs three aspects of lattice-based cryptography: the solvability of the Principal Ideal Problem, the freeness of modules over rings of integers, and t…

Module Lattice Security (Part II): Module Lattice Reduction via Optimal Sign Selection

Module Lattice Security (Part I): Unconditional Verification of Weber's Conjecture for k≤12

Module Lattice Security (Part I): Unconditional Verification of Weber's Conjecture for $k \leq 12$