Module Lattice Security (Part IV): Probabilistic Polynomial Quantum Attack on Module-LWE over 2-Power Cyclotomics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914598741868544 |
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| author | Luo, Ming-Xing |
| author_facet | Luo, Ming-Xing |
| contents | 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 factor satisfies $γ\le 21 < q/2=1664.5$ for ML-KEM-1024, with a success probability $\ge 0.99$. We apply a tower decomposition of the Principal Ideal Problem (PIP) through the chain $\Q\subset \Q(ζ_8)\subset\cdots\subset \Q(ζ_{2^k})$ which yields a polynomial-time quantum algorithm costing $O(n^3 \log^2 n)$ gates, $O(n^2 \log n)$ qubits, and poly$(n)$ classical bit operations. We extend the analysis to Falcon, Hawk, and NTRU over 2-power cyclotomic rings with polynomial-time quantum algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_17412 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Module Lattice Security (Part IV): Probabilistic Polynomial Quantum Attack on Module-LWE over 2-Power Cyclotomics Luo, Ming-Xing Quantum Physics Cryptography and Security Combinatorics Rings and Algebras 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 factor satisfies $γ\le 21 < q/2=1664.5$ for ML-KEM-1024, with a success probability $\ge 0.99$. We apply a tower decomposition of the Principal Ideal Problem (PIP) through the chain $\Q\subset \Q(ζ_8)\subset\cdots\subset \Q(ζ_{2^k})$ which yields a polynomial-time quantum algorithm costing $O(n^3 \log^2 n)$ gates, $O(n^2 \log n)$ qubits, and poly$(n)$ classical bit operations. We extend the analysis to Falcon, Hawk, and NTRU over 2-power cyclotomic rings with polynomial-time quantum algorithms. |
| title | Module Lattice Security (Part IV): Probabilistic Polynomial Quantum Attack on Module-LWE over 2-Power Cyclotomics |
| topic | Quantum Physics Cryptography and Security Combinatorics Rings and Algebras |
| url | https://arxiv.org/abs/2605.17412 |