Enhanced network security through algebraic cryptanalysis of elliptic curve cryptography

Ayyalasomayajula, Madan Mohan Tito; Ghanimi, Hayder M. A.; Manimaran, M.; Sonthi, Vijaya Krishna; Katiyan, Abrar Ahmed; Sengan, Sudhakar; Dadheech, Pankaj

doi:10.47974/JDMSC-2093

Open Access Research Article

Enhanced network security through algebraic cryptanalysis of elliptic curve cryptography

^*Madan Mohan Tito AyyalasomayajulaCorresponding authormail2tito@gmail.comDepartment of Computer Science College of Engineering Osmania UniversityHyderabad, Telangana, 500007, IndiaView full profile → , Hayder M. A. Ghanimihayder.alghanami@uowa.edu.iqDepartment of Information Technology College of Science University of Warith Al-Anbiyaa ; Department of Computer Science College of Computer Science and Information Technology University of Kerbala Department of Information Technology College of Science University of Warith Al-AnbiyaaKarbala, 5751, IraqView full profile → , M. Manimarandrmanimaranm@gmail.comDepartment of Cyber Security Easwari Engineering College Chennai, Tamil Nadu, 600089, IndiaView full profile → , Vijaya Krishna Sonthivijayakrishna1990@gmail.comDepartment of Computer Science and Engineering Koneru Lakshmaiah Education Foundation Department of Computer Science and Engineering Koneru Lakshmaiah Education FoundationVaddeswaram, Andhra Pradesh, 522502, IndiaView full profile → , Abrar Ahmed Katiyankaa406@yahoo.co.inDepartment of Computer Science and Engineering C Abdul Hakeem College of Engineering and Technology Vellore, Tamil Nadu, 632509, IndiaView full profile → , Sudhakar Sengansudhasengan@gmail.comDepartment of Computer Science and Engineering PSN College of Engineering and Technology Department of Computer Science and Engineering PSN College of Engineering and TechnologyTirunelveli, Tamil Nadu, 627152, IndiaView full profile → , Pankaj Dadheechpankajdadheech777@gmail.comDepartment of Computer Science and Engineering Swami Keshvanand Institute of Technology, Management & Gramothan (SKIT)Department of Computer Science & Engineering Swami Keshvanand Institute of Technology, Management & GramothanJaipur, Rajasthan, 302017, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 2219–2230Vol. 27Issue 7October 2024DOI: 10.47974/JDMSC-2093 Crossmark XML

Received:: 08 Mar 2024
Published Online:: 15 Oct 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2093
Pages:: 2219–2230

Abstract

The growing threat of cyberattacks has rendered the research of secure online systems an issue of concern. Elliptic Curve Cryptography (ECC) is an enhanced security benchmark that provides high-security levels with small key sizes. This work exhibits an Algebraic Cryptanalysis (AC) technique to evaluate and enhance ECC security systems with Gröbner Bases (GB). This paper investigates ECC vulnerabilities and recommends a technique for using GB to address the Elliptic Curve Discrete Logarithm Problem (ECDLP). Analysed amid conventional techniques such as Baby-Step Giant-Step (BS-GS), Pollard’s Rho (PR), and Pohlig-Hellman (PH), the approach was evaluated. The report proves that the proposed approach has a higher SR, averaging 96.33% throughout all tests.

Keywords

Mathematical modeling Ordinary differential equations A duopoly economy Market share

Subject Classifications

34A06

References

[1] M. Thakur, “Cyber security threats and countermeasures in digital age,” Journal of Applied Science and Education (JASE), vol. 4, no. 1, pp. 1-20 (2024).
[2] S. Gadde, G. S. Rao, V. S. Veesam, M. Yarlagadda, and R. S. M. Patibandla, “Secure data sharing in cloud computing: A comprehensive survey of two-factor authentication and cryptographic solutions,” Ingénierie des Systèmes d’Information, vol. 28, no. 6 (2023).
[3] Z. Vahdati, S. Yasin, A. Ghasempour, and M. Salehi, “Comparison of ECC and RSA algorithms in IoT devices,” Journal of Theoretical and Applied Information Technology, vol. 97, no. 16, p. 4293 (2019).
[4] J. J. Puthiyidam, S. Joseph, and B. Bhushan, “Temporal ECDSA: A timestamp and signature mask enabled ECDSA algorithm for IoT client node authentication,” Computer Communications, vol. 216, pp. 307-323 (2024).
[5] H. M. A. Ghanimi, T. Gopalakrishnan, G. J. Deol Sunny, K. Amarendra, P. Dadheech, and S. Sengan, “Chebyshev polynomial approximation in CNN for zero-knowledge encrypted data analysis,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-A, pp. 203–214 (2024). DOI: 10.47974/JDMSC-1880.
[6] H. M. A. Ghanimi, R. P. Melgarejo-Bolivar, A. Tumi-Figueroa, S. Ray, P. Dadheech, and S. Sengan, “Merkle-Damgård hash functions and blockchains: Securing electronic health records,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-A, pp. 237–248 (2024). DOI: 10.47974/JDMSC-1878.
[7] P. Vidya Sagar, H. M. A. Ghanimi, L. A. Prabhu, L. Raja, P. Dadheech, and S. Sengan, “Secure multi-party computation in deep learning: Enhancing privacy in distributed neural networks,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-A, pp. 249–259 (2024). DOI: 10.47974/JDMSC-1879.
[8] G. R. K. Rao, H. M. A. Ghanimi, V. Ramachandran, D. Al-Qahtani, P. Dadheech, and S. Sengan, “Enhanced security in federated learning by integrating homomorphic encryption for privacy-protected, collaborative model training,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-A, pp. 361–370 (2024). DOI: 10.47974/JDMSC-1891.
[9] R. J. Krishna, T. Gopalakrishnan, M. Divyapushpalakshmi, K. Amarendra, P. Dadheech, and S. Sengan, “Security and privacy concerns in social networks mathematically modified metaheuristic-based approach,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-A, pp. 371–382 (2024). DOI: 10.47974/JDMSC-1892.
[10] S. H. Nowfal, G. R. K. Rao, V. Velmurugan, S. Sengan, R. K. Bommisetti, and P. Dadheech, “Advancing viscoelastic material modeling: Tackling time-dependent behavior with fractional calculus,” Journal of Interdisciplinary Mathematics, vol. 27, no. 2, pp. 307–316 (2024). DOI: 10.47974/JIM-1827.
[11] P. V. Sagar, M. Rajyalaxmi, A. V. V. S. Subbalakshmi, S. Sengan, R. K. Bommisetti, and P. Dadheech, “Utilizing stochastic differential equations and random forest for precision forecasting in stock market dynamics,” Journal of Interdisciplinary Mathematics, vol. 27, no. 2, pp. 285–298 (2024). DOI: 10.47974/JIM-1822.

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