4 papers
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 -th cyclotomic rings. Using trace orthogonality of the power basis, we decompose a rank- mod…
quant-ph2026
Module Lattice Security (Part IV): Probabilistic Polynomial Quantum Attack on Module-LWE over 2-Power Cyclotomics
Ming-Xing Luo
We present a quantum attack on ML-KEM and related 2-power cyclotomic lattice schemes. Combining with Parts I-III, we provide an algorithm and verify the resulting approximation fac…
cs.DS2026
Module Lattice Security (Part III): Structured CVP Distance on the Log-Unit Lattice
Ming-Xing Luo
We prove that the CVP distance from a random short ring element to the log-unit lattice of $\Q(ζ_{2^k})$ converges to as . W…
cs.CR2026
Module Lattice Security (Part I): Unconditional Verification of Weber's Conjecture for
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…