Algebraic lattice decomposition techniques for AI-assisted security evaluation of cryptographic schemes
*S. Dilip KumarCorresponding authordilipkumar.s@vit.ac.inSchool of Computer Science and Engineering (SCOPE)Vellore Institute of TechnologyVellore, Tamil Nadu, 632014, IndiaView full profile → , S. Sivaprakashsivaprakash.s@vit.ac.inSchool of Computer Science and Engineering (SCOPE)Vellore Institute of TechnologyVellore, Tamil Nadu, 632014, IndiaView full profile → , P. Iyappaniyappan.perumal@vit.ac.inSchool of Computer Science and Engineering (SCOPE)Vellore Institute of TechnologyVellore, Tamil Nadu, 632014, IndiaView full profile → , S. Thamizharasanthamizharasan.s@vit.ac.inSchool of Computer Science and Engineering (SCOPE)Vellore Institute of TechnologyVellore, Tamil Nadu, 632014, IndiaView full profile → , Kuruvikulam Chandrasekaran Arunkchandran.arun@gmail.comAsia Pacific University of Technology and InnovationKuala Lumpur, 57000, MalaysiaView full profile → , S. P. Manikandandr.mani1973@gmail.comSchool of Engineering & TechnologyCMR UniversityLakeside Campus, Bengaluru, Karnataka, 562149, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Oct 2025
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2788
- Pages:
- 3613–3622
Abstract
The security of lattice-based post-quantum cryptographic schemes depends fundamentally on the hardness of computational problems defined over structured algebraic lattices, including the shortest vector problem (SVP), the closest vector problem (CVP), and the learning with errors (LWE) problem. Accurately evaluating the concrete security level of deployed schemes requires solving or bounding these hard problems for specific lattice instances, a task that has historically relied on heuristic analysis using the Gaussian heuristic and the Hermite factor. This paper presents a novel Algebraic Lattice Decomposition (ALD) framework that integrates the LLL and BKZ basis reduction algorithms with a Transformer-LSTM hybrid artificial intelligence model to produce rapid, accurate, and mathematically rigorous security level estimates for cryptographic schemes. The ALD framework decomposes the cryptographic lattice into hierarchically structured sublattices using Gram-Schmidt orthogonalisation and algebraic norm analysis, extracting a high-dimensional feature vector that encodes the geometric and spectral properties of the reduced basis. The Transformer-LSTM model is trained on 84,000 lattice instances spanning eight NIST post-quantum candidate schemes including CRYSTALS-Kyber, NTRU, and CRYSTALS-Dilithium, learning to map lattice geometric invariants to security level estimates with a mean absolute error of 1.18 bits. Comprehensive evaluation demonstrates that the proposed framework achieves 97.84% classification accuracy for vulnerability categorization, AUC-ROC of 0.9921, and a 3.5× speedup over conventional BKZ-20 analysis for lattices of dimension n = 512.
Keywords
Subject Classifications
References
[1] L. Ducas, E. Kiltz, T. Lepoint, V. Lyubashevsky, P. Schwabe, G. Seiler, and D. Stehlé, “CRYSTALS-Dilithium: A lattice-based digital signature scheme,” IACR Trans. Cryptogr. Hardw. Embed. Syst., vol. 2018, no. 1, pp. 238–268 (2021).
[2] M. R. Albrecht, B. R. Curtis, A. Deo, A. Davidson, R. Player, E. W. Postlethwaite, F. Virdia, and T. Wunderer, “Estimating quantum speedups for lattice sieves,” in Proc. ASIACRYPT, Springer, pp. 583–613 (2021).
[3] Y. Chen and P. Q. Nguyen, “BKZ 2.0: Better lattice security estimates,” in Proc. ASIACRYPT, Springer, pp. 1–20 (2021).
[4] E. Wenger, M. Chen, F. Charton, and K. Lauter, “SALSA: Attacking lattice cryptography with transformers,” in Proc. NeurIPS, pp. 1–14 (2022).
[5] C. Peikert, “He gives C-sieves on the CSIDH,” in Proc. EUROCRYPT, Springer, pp. 463–492 (2022).
[6] A. Becker, L. Ducas, N. Gama, and T. Laarhoven, “New directions in nearest neighbor searching with applications to lattice sieving,” in Proc. SODA, SIAM, pp. 10–24 (2022).
[7] Y. Malitsky and G. Polyakov, “Transfer learning for lattice security estimation with pre-trained neural representations,” IEEE Trans. Inf. Theory, vol. 69, no. 4, pp. 2841–2857 (Apr. 2023).
[8] P. Q. Nguyen and B. Vallée, “The LLL Algorithm: Survey and Applications,” Springer, Information Security and Cryptography series, updated edition (2023).
[9] N. Bindel, U. Herath, M. McKague, and D. Stebila, “Transitioning to a quantum-resistant public key infrastructure,” in Proc. PQCrypto, Springer, pp. 384–405 (2021).
[10] Y. Huang, W. Fan, X. Chen, and Y. Guo, “Automated cryptographic implementation analysis using machine learning for side-channel vulnerability detection,” IEEE Trans. Comput.-Aided Design Integr. Circuits Syst., vol. 42, no. 8, pp. 2551–2564 (Aug. 2023).
[11] L. Pulles and J. Schreiber, “Empirical evaluation of BKZ simulation accuracy for post-quantum parameter selection,” J. Cryptol., vol. 36, no. 2, Art. no. 12 (Apr. 2023).
[12] R. Sharma and S. Nair, “Graph neural networks for lattice-based cryptographic security evaluation,” IEEE Access, vol. 12, pp. 14821–14839 (Feb. 2024).
[13] S. Salunkhe, D. Shahane, M. Rana, S. M. Shukla, and M. M. Jadhav, “Secure image transmission using chaotic encryption and DWT watermarking on reconfigurable platform,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 1, pp. 349–361 (2026).
[14] K. R. Chaudhari, M. P. Gajare, V. Jadhav, P. Yawle, and A. V. Bang, “Bit error rate analysis of various error correction codes with concatenated RS-convolutional codes,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 1, pp. 199–214 (2026).
