A novel development of OTRU cryptosystem
Resumen
In the light of the tremendous development in data exchanging, maintaining its confidentiality has become extremely vital when transferring it in an insecure medium, so there is a constant need to develop encryption systems. One of these encryption systems is NTRU, which was developed by OTRU encryption. In this paper, we presented a development of OTRU, which is called KSQOT, by using KAH-octo algebra with partial coefficients of quaternion algebra instead of octonion algebra (a mix between octonion algebra and quaternion algebra) with eight dimensions but with sixteen partial elements for each element and different mathematical constructions of the phases (key generation, encryption, and decryption) of the system which allude a very high level of security by augmenting the private keys with the public key and an acceptable speed by the number of mathematical operations used in constructing the method.
Descargas
Citas
J. Hoffstein, J. Pipher, J. H. Silverman, D. Lieman, J. Pipher, and J. H. Silverman, “NTRU: A ring-based public key cryptosystem,” in International algorithmic number theory symposium, Springer, 1998, pp. 267–288.
P. Gaborit, J. Ohler and P. Soli, “CTRU, a polynomial Analogue of NTRU,” INRIA. Rapport de recherche, no. 4621, 2002.
M. Coglianese and B. Goi, “MaTRU: A new NTRU based cryptosystem”, Springer Verlag Berlin Heidelberg, vol. 3797 p.p. 232-243, 2005.
E. Malecian, A. Zakerolhsooeini and A. Mashatan, “QTRU: Quaternionic Version of the NTRU Public-Key Cryptosystems,” The ISC Int’l Journal of Information Security, vol. 3, no. 1, pp. 9-42, 2011.
B. Y. Hussein, Equivalent Locally Martingale Measure for the DeflatorProcess on Ordered Banach Algebra, Journal of Mathematics, Vol. 2020, pp. 1-7, 2020.
H. A. Wshayeh and B.Y. Hussein, On δ-characterization in symmetric Δ-Banach algebra with Hermitian properties, AIP Conference Proceedings, Vol. 2386. pp. 1-8, 2022
D. Eberly, “Quaternion algebra and calculus,” Magic Softw. Inc, vol. 26, pp. 1–8, 2002.
E. Malekian and A. Zakerolhosseini, “OTRU: A non-associative and high speed public key cryptosystem,” in 2010 15th CSI International Symposium on Computer Architecture and Digital Systems, IEEE, 2010, pp. 83–90.
N. Alsaidi, M. Saed, A. Sadiq, and A. A. Majeed “An improved NTRU Cryptosystem via Commutative Quaternions Algebra,” Int’l Conf. Security and Management (SAM’15), 2015, pp. 198–203.
V. Lyubashevsky, G. Seiler, “NTTRU: Truly Fast NTRU Using NTT,” IACR Transactions on Cryptographic Hardware and Embedded Systems, no. 3, pp. 180-201, 2019.
H. H. Abo-Alsood and H. R. Yassein, “Design of an alternative NTRU Encryption with High Secure and Efficient,” Int. J. Math. Comput. Sci., vol. 16, no. 4, pp. 1469–1477, 2021.
S. H. Shahhadi and H. R. Yassein, “NTRsh: A New Secure Variant of NTRUEncrypt Based on Tripternion Algebra,” Journal of Physics: Conference Series, 2021, pp. 1–6.
S. H. Shahhadi and H. R. Yassein, “A New Design of NTRU Encrypt-analog Cryptosystem with High Security and Performance Level via Tripternion Algebra,” Int. J. Math. Comput. Sci., vol. 16, no. 4, pp. 1515–1522, 2021.
H. H. Abo-Alsood and H. R. Yassein, “Analogue to NTRU public key cryptosystem by multi-dimensional algebra with high security,” AIP Conference Proceedings, AIP Publishing LLC, 2022, pp. 1–6.
S. H. Shahhadi and H. R. Yassein, “An innovative tripternion algebra for designing NTRU-like cryptosystem with high security,” AIP Conference Proceedings, AIP Publishing, 2022, pp. 1–6.
Hassan Rashed Yassein, Hany Nasry Zaky, Hadeel Hadi Abo-Alsoo, Ismail A Mageed, Wageda I El-Sobky, QuiTRU: Design Secure Variant of Ntruencrypt Via a New Multi-Dimensional Algebra, Applied Mathematics and Information Sciences, Vol. 17, no. 1, pp. 49-53, 2023
K. A. Hassoon and H. R. Yassein, “Proposed Multi-Dimensional Algebra,” Int. J. Math. Comput. Sci., vol. 19, no. 3, pp. 765–770, 2024.
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática

Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).



