A new public key cryptosystem based on the non-commutative ring R
*Bilel SelikhCorresponding authorbilel.selikh@univ-msila.dzDepartment of Mathematics Laboratory of Pure and Applied Mathematics Mohamed Boudiaf University of M’sila P. O. Box 166 IchbiliaM’sila, 28000, AlgeriaView full profile → , Abdelhakim Chillaliabdelhakim.chillali@usmba.ac.maDepartment of Mathematics, Physics & Computer Science Polydisciplinary Faculty Laboratory of Engineering Sciences Sidi Mohamed Ben Abdellah UniversityTaza, MoroccoView full profile → , Douadi Mihoubidouadi.mihoubi@univ-msila.dzDepartment of Mathematics Laboratory of Pure and Applied Mathematics Mohamed Boudiaf University of M’sila P. O. Box 166 IchbiliaDepartment of Mathematics Laboratory of Pure and Applied Mathematics M’sila UniversityM’sila, 28000, AlgeriaView full profile → , Nacer Ghadbanenasser.ghedbane@univ-msila.dzDepartment of Mathematics Laboratory of Pure and Applied Mathematics Mohamed Boudiaf University of M’sila P. O. Box 166 IchbiliaM’sila, 28000, AlgeriaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Aug 2021
- Published Online:
- 24 Jan 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1573
- Pages:
- 75–93
Abstract
Keywords
Subject Classifications
References
[1] Boulbot A., Chillali A. and Mouhib A., Cryptographic Protocols on the non commutative Ring R, International Journal of Mathematical and Computational Methods, 2017, 2, 138-141. DOI: 10.1109/ISACS48493.2019.9068892.
[2] Boyd C. and Mathuria A., Protocols for Authentication and Key Establishment, Information Security and Cryptography Series; Springer-Verlag, Heidelberg, 2003.
[3] Chatterjee A. and Aung K. M. M., Fully Homomorphic Encryption in Real World Applications, Computer Architecture and Design Methodologies, Springer Nature, Singapore, 2019. DOI: 10.1007/978-981-13-6393-1.
[4] Diffie W. and Hellman M., New directions in cryptography, IEEE Transactions on Information Theory, 1976, 22(6), 644-654. DOI: 10.1109/TIT.1976.1055638.
[5] Elhassani M., Boulbot A., Cillali A. and Mouhib A., Fully homomorphic encryption scheme on a non-Commutative ring R, International Conference on Intelligent Systems and Advanced Computing Sciences (ISACS), 2019. DOI: 10.1109/ISACS48493.2019.9068892.
[6] Koblitz N., Elliptic curve cryptosystems, Mathematics of Computation, 1987, 48(177), 203-209. DOI: 10.1090/S0025-5718-1987-0866109-5.
[7] Miller V., Use of elliptic curves in cryptography, CRYPTO’85, LNCS 218, Springer, 1986, 417-426. DOI: 10.1007/3-540-39799-X_31.
[8] Meshram C. and Li X. , New efficient key authentication protocol for public key cryptosystem using DL over multiplicative group, Journal of Information and Optimization Sciences, 2018, 39(2), 391-400. DOI: 10.1080/02522667.2017.1411013.
[9] Rivest R. L., Adleman L. and Dertouzos M. L., On data banks and privacy homomorphisms, Foundations of Secure Computation 1978, 11(4), 169-180.
[10] Sahmoudi M. and Chillali A., Key exchange over particular algebraic closure ring, Tatra Mountains Mathematical Publications, 2017, 70, 151-162. DOI: 10.1515/tmmp-2017-0024.
[11] Selikh B., Chillali A., Mihoubi D. and Ghadbane N., ECC over the ring by using two methods, Tbilisi Mathematical Journal, 2021, 14(3), 213-223. DOI: 10.32513/tmj/19322008155.
[12] Selikh B., Mihoubi D. and Ghadbane N., Classification of elements in elliptic curve over the ring Discussiones Mathematicae General Algebra and Applications, 2021, 41(2), 283-298. DOI: 10.7151/dmgaa.1371.
[13] Sundarayya P. and Vara Prasad G., A public key cryptosystem using Affine Hill Cipher under modulation of prime number, Journal of Information and Optimization Sciences, 2019, 40(4), 919-930. DOI: 10.1080/02522667.2018.1470751.




