Attack on lattice shortest vector problem using K-Nearest Neighbour (original) (raw)

Abstract

Lattice-based cryptography is now the most effective and adaptable branch of post-quantum cryptography. The prime number factoring assumption or the presumption that the discrete logarithm problem is intractable are the two assumptions that underlie nearly all cryptographic security systems. Lattice-based cryptography has recently gained popularity to improve security as the world prepares for quantum computing. Lattices are used to secure the systems; however, one of the problems is the Shortest vector problem. In this work, we addressed the attack on lattice problems, especially two-dimensional, four-dimensional, and ten-dimensional, with the help of the machine learning algorithm K-Nearest Neighbour (KNN). Results and analysis findings demonstrate that the suggested approach can achieve accuracy of upto 78% and 58% on self-prepared datasets over two-dimensional and ten- dimensional, respectively.

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Data availability

The data set generated and/or analyzed during the current study is available upon reasonable request from the corresponding author. However, data sets are available as open source.

References

  1. Bandara, H., Herath, Y., Weerasundara, T., Alawatugoda, J.: On advances of lattice-based cryptographic schemes and their implementations. Cryptography 6(56), 1–22 (2022). https://doi.org/10.3390/cryptography6040056
    Article Google Scholar
  2. Sood, N.: Cryptography in Post Quantum Computing Era. (2024). Online available at: https://www.researchgate.net/publication/377696294_Cryptography_in_Post_Quantum_Computing_Era. Accessed 22 Janu 2024
  3. Stanley, M., Gui, Y., Unnikrishnan, D., Hall, S.R.G., Fatadin, I.: Recent progress in quantum key distribution network deployments and standards. In: National Physical Laboratory Joint Symposium on Quantum Technologies, Journal of Physics: Conference Series. 2416: 1-14 (2022). https://doi.org/10.1088/1742-6596/2416/1/012001
  4. Singh, A., Padhye, S.: A lattice-based key exchange protocol over NTRU-NIP. In: Roy, B.K., Chaturvedi, A., Tsaban, B., Hasan, S.U. (eds) Cryptology and Network Security with Machine Learning. ICCNSML 2022. Algorithms for Intelligent Systems. Springer, Singapore, 325–334 (2023). https://doi.org/10.1007/978-981-99-2229-1_27
  5. Sun, Z., Gu, C., Zheng, Y.: A review of sieve algorithms in solving the shortest lattice vector problem. In IEEE Access 8, 190475–190486 (2020). https://doi.org/10.1109/ACCESS.2020.3031276
    Article Google Scholar
  6. Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coefficients. Math. Ann. 261(4), 515–534 (1982). https://doi.org/10.1007/BF01457454
    Article MathSciNet Google Scholar
  7. Lagarias, J.C.: Knapsack public key cryptosystems and diophantine approximation. In: Advances in Cryptology, 3–23 (1983). https://doi.org/10.1007/978-1-4684-4730-9_1
  8. Micciancio, D., Regev, O. Lattice-based Cryptography, pp. 1–33, Online available at: https://cims.nyu.edu/~regev/papers/pqc.pdf (2008). Accessed 8 Feb 2024
  9. Zhang, J., Zhang, Z.: Lattice-Based Cryptosystems-A Design Perspective, vol. XIII, p. 174. Springer Singapore (2020)
    Book Google Scholar
  10. Bandara, H., Herath, Y., Weerasundara, T., Alawatugoda, J.: On advances of lattice-based cryptographic schemes and their implementations. Cryptography MDPI. 6(56), 1–22 (2022). https://doi.org/10.3390/cryptography6040056
    Article Google Scholar
  11. Singh, S.P., Chaurasia, B.K., Pal, A., Gupta, S., Tripathi, T.: Lattice reduction using K-means algorithm. EAI Endorsed Trans. Scalable Inf. Syst. 1–11 (2024). https://doi.org/10.4108/eetsis.339492
  12. Stehlé, D., Steinfeld, R.: Making NTRU as secure as worst-case problems over ideal lattices. In: K. G. Paterson (Ed.), Advances in Cryptology - EUROCRYPT 2011, 30th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Proceedings 6632: 27–47, (2011). https://doi.org/10.1007/978-3-642-20465-4_4
  13. Guo, G., Wang, H., Bell, D., Bi, Y., Greer, K.: KNN model-based approach in classification. In: Lecture Notes in Computer Science, pp. 986–996 (2023). https://doi.org/10.1007/978-3-540-39964-3_62
  14. Cunningham, P., Delany, S.J.: k-Nearest Neighbour Classifiers: 2nd Edition (with Python examples), Online available at: https://arxiv.org/pdf/2004.04523.pdf. (2020). Accessed 8 Feb 2024
  15. Li, J., Nguyen, P.Q.: A complete analysis of the BKZ lattice reduction algorithm, 1–45, Online available at: https://eprint.iacr.org/2020/1237.pdf. Accessed 29 Mar 2023
  16. Parthasarathy, G., Chatterji, B.N.: A class of new KNN methods for low sample problems. In IEEE Trans. Syst. Man Cybern. 20(3), 715–718 (1990). https://doi.org/10.1109/21.57285
    Article Google Scholar
  17. Helfrich, B.: Algorithms to construct Minkowski reduced and hermite reduced lattice bases. Theoret. Comput. Sci.. Comput. Sci. 41, 125–139 (1985). https://doi.org/10.1016/0304-3975(85)90067-2
    Article MathSciNet Google Scholar
  18. Seber, A.F., Lee, A.J.: Linear Regression Analysis, pp. 1–583. Wiley (2023)
    Google Scholar
  19. Duan, M.: Innovative compressive strength prediction for recycled aggregate/concrete using K-nearest neighbors and meta-heuristic optimization approaches. J. Eng. Appl. Sci. 71(15), 1–16 (2024). https://doi.org/10.1186/s44147-023-00348-9
    Article Google Scholar
  20. Python Language, Online available at: https://www.python.org/. Accessed 29 Mar 2023

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Acknowledgements

We would like to express our gratitude to Dr. Bhupendra Singh, Scientist –F, CAIR, DRDO, C V Raman Nagar, Bangalore, Karnataka, India for his valuable contributions and insights that enriched this research.

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The authors are not received funding from any of the sources.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Pranveer Singh Institute of Technology, Kanpur, India
    Shaurya Pratap Singh, Brijesh Kumar Chaurasia, Tanmay Tripathi, Ayush Pal & Siddharth Gupta

Authors

  1. Shaurya Pratap Singh
  2. Brijesh Kumar Chaurasia
  3. Tanmay Tripathi
  4. Ayush Pal
  5. Siddharth Gupta

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The idea and problem formulation along with proposed solution, result analysis, and by corresponding author & supervisor, and verifies by all other authors.

Corresponding author

Correspondence toBrijesh Kumar Chaurasia.

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Singh, S.P., Chaurasia, B.K., Tripathi, T. et al. Attack on lattice shortest vector problem using K-Nearest Neighbour.Iran J Comput Sci 7, 515–531 (2024). https://doi.org/10.1007/s42044-024-00184-x

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