Dihedral group order 12 noncommutative cryptography primitive generations
Gautam Kumargautam.kumar21ujrb@jaipur.manipal.eduDepartment of Artificial Intelligence and Machine Learning Manipal University Jaipur Jaipur, Rajasthan, 303007, IndiaView full profile → , Sonu Sharmasonu.sharma@poornima.edu.inDepartment of Computer Science and Engineering Poornima University Jaipur, Rajasthan, 303905, IndiaView full profile → , *Vijay Shankar SharmaCorresponding authorvijayshankar.sharma@jaipur.manipal.eduDepartment of Computer and Communication Engineering Manipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Dharm Singh Jatdharmsingh63@hotmail.comDepartment of Computer Science Namibia University of Science & TechnologyDepartment of Computer Science Namibia University of Science and Technology (NUST)Windhoek, 13388, NamibiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Nov 2024
- Published Online:
- 30 Aug 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2422
- Pages:
- 2049–2058
Abstract
Keywords
Subject Classifications
References
[1] V. V. Anh and K. S. Govindarajan, “On Noncommutative Cryptographic Schemes Using Semigroup Structures,” Journal of Discrete Mathematical Sciences and Cryptography, Vol. 16, No. 2–3, pp. 145–158 (2013). DOI: 10.1080/09720529.2013.11891245
[2] Peter W. Shor, “Algorithms for Quantum Computation: Discrete logarithms and Factorings,” In Proceedings of the 35th Annual Symposium on Foundations of Computer Science, pp. 124-134 (1994), DOI:10.1109/SFCS.1994.365700
[3] Alexei Kitaev, “Quantum Measurements and the Abelian Stabilizer Problem. Electronic Colloquium on Computational Complexity,” Vol. 3 (1996), DOI: http://eccc.hpi-web.de/eccc-reports/1996/TR96-003/index.html
[4] John Proos and Christof Zalka, “Shor’s Discrete Logarithm Quantum Algorithm for Elliptic Curve,” Quantum Information & Computation, Vol. 3, pp. 317-344 (2003), DOI: http://dl.acm.org/citation.cfm?id=2011531
[5] P. Vijayakumar and C. Duraisamy, “Quantum Resistant Noncommutative Public Key Cryptography Using Matrix Groups,” Journal of Discrete Mathematical Sciences and Cryptography, Vol. 21, No. 5, pp. 1095–1110 (2018). DOI: 10.1080/09720529.2018.1492247
[6] Martin Rotteler, “Quantum Algorithm: A Survey of Some Recent Results,” Information Forensic Entw., Vol. 21, pp. 3-20 (2006), DOI: http://link.springer.com/content/pdf/10.1007%2Fs00450-006-0008-7.pdf
[7] Iris Anshel, Michael Anshel, and Dorian Goldfeld, “A Linear Time Matrix Key Agreement Protocol over Small Finite Fields,” AAECC (2006), DOI: http://link.springer.com/content/pdf/10.1007/s00200-006-0001-1.pdf
[8] Dmitriy N. Moldovyan and Nikolay A. Moldovyan, “A New Hard Problem over Non-commutative Finite Groups for Cryptographic Protocols,” Lecture Notes in Computer Science, Springer-Verlag Heidelberg, New York. Vol. 6258, pp. 183-194, Vol. 6258 (2010), DOI: 10.1007/978-3-642-14706-7_14
[9] James Hughes and Allen Tannenbaum, “Length-Based Attacks for Certain Group Based Encryption Rewriting Systems,” Institute for Mathematics and Its Application (2000), DOI: http://purl.umn.edu/3443
