A Novel Approach to Bit-Flipping Threshold Selection with Particle Swarm Optimization in the QC-MDPC-McEliece Cryptosystem

[1] J. Buchmann, Introduction to Cryptography, vol. 335. Springer, 2004. BuchmannJ. Introduction to Cryptography 335 Springer 2004 Search in Google Scholar

[2] P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Review, vol. 41, pp. 303–332, 1999. https://arxiv.org/pdf/quant-ph/9508027 ShorP. W. “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Review 41 303 332 1999 https://arxiv.org/pdf/quant-ph/9508027 Search in Google Scholar

[3] D. J. Bernstein and T. Lange, “Post-quantum cryptography,” Nature, vol. 549, pp. 188–194, 2017. BernsteinD. J. LangeT. “Post-quantum cryptography,” Nature 549 188 194 2017 Search in Google Scholar

[4] R. J. McEliece, “A public-key cryptosystem based on algebraic coding theory,” Coding Thv, vol. 4244, pp. 114–116, 1978. McElieceR. J. “A public-key cryptosystem based on algebraic coding theory,” Coding Thv 4244 114 116 1978 Search in Google Scholar

[5] R. Misoczki, J. P. Tillich, N. Sendrier, and P. S. Barreto, “MDPC-McEliece: New McEliece variants from moderate density parity-check codes,” in 2013 IEEE International Symposium on Information Theory, IEEE, 2013, pp. 2069–2073. https://inria.hal.science/hal-00870929v1/document MisoczkiR. TillichJ. P. SendrierN. BarretoP. S. “MDPC-McEliece: New McEliece variants from moderate density parity-check codes,” in 2013 IEEE International Symposium on Information Theory IEEE 2013 2069 2073 https://inria.hal.science/hal-00870929v1/document Search in Google Scholar

[6] N. Sendrier and V. Vasseur, “On the decoding failure rate of QC-MDPC bit-flipping decoders,” in Post-Quantum Cryptography: 10th International Conference, PQCrypto 2019, Chongqing, China, May 8–10, 2019 Revised Selected Papers, vol. 10, Springer, 2019, pp. 404–416. https://inria.hal.science/hal-03139797/document SendrierN. VasseurV. “On the decoding failure rate of QC-MDPC bit-flipping decoders,” in Post-Quantum Cryptography: 10th International Conference, PQCrypto 2019 Chongqing, China May 8–10, 2019 Revised Selected Papers, vol. 10, Springer, 2019, 404 416 https://inria.hal.science/hal-03139797/document Search in Google Scholar

[7] V. Vasseur, “Post-quantum cryptography: A study of the decoding of QC-MDPC codes,” Ph.D dissertation, Université de Paris, Paris, France, Jun. 2021. VasseurV. “Post-quantum cryptography: A study of the decoding of QC-MDPC codes,” Ph.D dissertation, Université de Paris Paris, France Jun. 2021 Search in Google Scholar

[8] M. R. Nosouhi, S. W. A. Shah, L. Pan, and R. Doss, “Bit Flipping Key Encapsulation for the Post-Quantum Era,” IEEE Access, vol. 11, pp. 56181–56195, 2023. NosouhiM. R. ShahS. W. A. PanL. DossR. “Bit Flipping Key Encapsulation for the Post-Quantum Era,” IEEE Access 11 56181 56195 2023 Search in Google Scholar

[9] A. Kichna, A. Farchane, and S. Hakimi, “Analyzing the impact of thresholds in bit-flipping decoding for qc-mdpc based mceliece cryptosystems,” 2024 7th International Conference on Advanced Communication Technologies and Networking (CommNet), pp. 1–5, 2024. KichnaA. FarchaneA. HakimiS. “Analyzing the impact of thresholds in bit-flipping decoding for qc-mdpc based mceliece cryptosystems,” 2024 7th International Conference on Advanced Communication Technologies and Networking (CommNet) 1 5 2024 Search in Google Scholar

[10] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN'95-International Conference on Neural Networks, IEEE, 1995, pp. 1942–1948. KennedyJ. EberhartR. “Particle swarm optimization,” in Proceedings of ICNN'95-International Conference on Neural Networks IEEE 1995 1942 1948 Search in Google Scholar

[11] J. Nayak, H. Swapnarekha, B. Naik, G. Dhiman, and S. Vimal, “25 years of particle swarm optimization: Flourishing voyage of two decades,” Archives of Computational Methods in Engineering, vol. 30, pp. 1663–1725, 2023. NayakJ. SwapnarekhaH. NaikB. DhimanG. VimalS. “25 years of particle swarm optimization: Flourishing voyage of two decades,” Archives of Computational Methods in Engineering 30 1663 1725 2023 Search in Google Scholar

[12] T. M. Shami, A. A. El-Saleh, M. Alswaitti, Q. Al-Tashi, M. A. Summakieh, and S. Mirjalili, “Particle swarm optimization: A comprehensive survey,” IEEE Access, vol. 10, pp. 10031–10061, 2022. ShamiT. M. El-SalehA. A. AlswaittiM. Al-TashiQ. SummakiehM. A. MirjaliliS. “Particle swarm optimization: A comprehensive survey,” IEEE Access 10 10031 10061 2022 Search in Google Scholar

[13] R. Gallager, “Low-density parity-check codes,” IRE Transactions on Information Theory, vol. 8, pp. 21–28, 1962. GallagerR. “Low-density parity-check codes,” IRE Transactions on Information Theory 8 21 28 1962 Search in Google Scholar

[14] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, vol. 16. Elsevier, 1977. MacWilliamsF. J. SloaneN. J. A. The Theory of Error-Correcting Codes 16 Elsevier 1977 Search in Google Scholar

[15] A. Janoska, “MDPC decoding algorithms and their impact on the McEliece cryptosystem,” in 2018 Federated Conference on Computer Science and Information Systems (FedCSIS), IEEE, 2018, pp. 1085–1089. https://annals-csis.org/proceedings/2018/drp/pdf/99.pdf JanoskaA. “MDPC decoding algorithms and their impact on the McEliece cryptosystem,” in 2018 Federated Conference on Computer Science and Information Systems (FedCSIS) IEEE 2018 1085 1089 https://annals-csis.org/proceedings/2018/drp/pdf/99.pdf Search in Google Scholar

[16] A. P. Engelbrecht, Computational Intelligence: An Introduction. John Wiley & Sons, 2007. EngelbrechtA. P. Computational Intelligence: An Introduction John Wiley & Sons 2007 Search in Google Scholar