Proposed development of RSA via new multidimensional algebra
*Dalael Saad Abdul-ZahraCorresponding authordalael20175@gmail.comDepartment of MathematicsFaculty of Education for GirlsUniversity of KufaKufa, Al Najaf, 540011, Iraq0000-0001-5949-0671View full profile → , Hassan Rashed Yasseinhassan.yassein@qu.edu.iqDepartment of MathematicsFaculty of EducationUniversity of Al-QadisiyahAl-Diwaniya, 58003, Iraq0000-0002-6788-0247View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 09 May 2024
- Published Online:
- 21 Mar 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2022
- Pages:
- 375–380
Abstract
Keywords
Subject Classifications
References
[1] B. N. Abbas and H. R. Yassein, “A high-security encryption based on hexadecnion polynomials,” Int. J. Math. Comput. Sci., vol. 19, no. 1, pp. 37-40 (2024).
[2] B. N. Abbas and H. R. Yassein, “Design of an alternative to polynomial modified RSA algorithm,” Int. J. Math. Comput. Sci., vol. 19, no. 3, pp. 693-696 (2024).
[3] I. B. Gafitoiu, Polynomial based RSA, B. Sc. Thesis, Linnaeus University, Sweden (2015).
[4] B. Imine, N. Hadj-Said, and A. Ali-Pacha, “New McEliece cryptosystem based on non-permutation equivalent polar codes,” J. Discrete Math. Sci. Cryptogr., Aug. (2021). [Online]. Available: https://doi.org/10.1080/09720529.2021.1933706.
[5] B. Ivy, P. Mandiwa, and M. Kumar, “A modified RSA cryptosystem based on ‘n’ prime numbers,” Int. J. Eng. Comput. Sci., vol. 1, no. 2, pp. 63-66 (2012).
[6] M. Mumtaz and L. Ping, “Forty years of attacks on the RSA cryptosystem: A brief survey,” J. Discrete Math. Sci. Cryptogr., vol. 22, no. 1, pp. 9-29 (2019). [Online]. Available: https://doi.org/10.1080/09720529.2018.1564201.
[7] A. Nitaj and E. Fouotsa, “A new attack on RSA and Demytko’s elliptic curve cryptosystem,” J. Discrete Math. Sci. Cryptogr., vol. 22, no. 3, pp. 391-409 (2019). [Online]. Available: https://doi.org/10.1080/09720529.2019.1587827.
[8] R. L. Rivest, A. Shamir, and L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems,” Commun. ACM, vol. 21, no. 2, pp. 120-126 (1978). [Online]. Available: https://doi.org/10.1145/359340.359342.
[9] M. C. Semmouni, A. Nitaj, and M. Belkasmi, “Cryptanalysis of RSA with smooth prime sum,” J. Discrete Math. Sci. Cryptogr., vol. 26, no. 8, pp. 1-21 (2022). [Online]. Available: https://doi.org/10.1080/09720529.2021.2000152.
[10] H. S. Salman and H. R. Yassein, “An innovative HSS algebra for designing a secure like-NTRU encryption,” Math. Statist. Eng. Appl., vol. 71, no. 4, pp. 6098-6113 (2022). [Online]. Available: https://doi.org/10.17762/msea.v71i4.1208.
[11] H. R. Yassein and N. M. Al-Saidi, “BITRU: Binary version of the NTRU public key cryptosystem via binary algebra,” Int. J. Adv. Comput. Sci. Appl., vol. 7, no. 11, pp. 1-6 (2016). [Online]. Available: https://doi.org/10.14569/IJACSA.2016.071101.
[12] H. R. Yassein and N. M. Al-Saidi, “HXDTRU cryptosystem based on hexadecnion algebra,” Proc. 5th Int. Cryptol. Inf. Security Conf., Kota Kinabalu, Malaysia (2016).
[13] H. R. Yassein, N. M. G. Al-Saidi, and A. K. Farhan, “A new NTRU cryptosystem outperforms three highly secured NTRU-analog systems through an innovational algebraic structure,” J. Discrete Math. Sci. Cryptogr., vol. 25, no. 2, pp. 523-542 (2020). [Online]. Available: https://doi.org/10.1080/09720529.2020.1741218.
[14] H. R. Yassein and H. A. Ali, “HUDTRU: An enhanced NTRU for data security via quintuple algebra,” Int. J. Math. Comput. Sci., vol. 18, no. 2, pp. 199-204 (2023).
[15] A. H. Alwan, “Small intersection graph of subsemimodules of a semimodule,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2022, no. 1, pp. 15-22 (2022).
[16] S. Ediza, M. Cancana, and M. R. Farahani, “Eccentric connectivity and connective eccentricity indices of generalized Petersen graphs,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2021, no. 1, pp. 1-6 (2021).
[17] R. Ponraj, S. Prabhu, and M. Sivakumar, “Pair mean cordial labeling of total graph of some graphs and prism related graphs,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2024, no. 2, pp. 181-192 (2024).
[18] F. O. Oduol and I. O. Okoth, “Counting vertices among all noncrossing trees by levels and degrees,” Commun. Combinatorics Cryptogr. Comput. Sci., vol. 2024, no. 2, pp. 193-212 (2024).
