Encryption and decryption scheme through signed Cayley graph
Obaidullah Wardakobaid.wardak22@live.comDepartment of MathematicsSouth Asian UniversityNew Delhi, Delhi, 110068, India0000-0002-2410-1960View full profile → , Sandeep Kumarssulakh.94@gmail.comDepartment of MathematicsSouth Asian UniversityNew Delhi, Delhi, 110068, India0009-0005-7107-3914View full profile → , *Deepa SinhaCorresponding authordeepasinha2001@gmail.comDepartment of MathematicsSouth Asian UniversityNew Delhi, Delhi, 110068, India0000-0002-5695-5282View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 04 Jul 2023
- Published Online:
- 20 Feb 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2201
- Pages:
- 2811–2825
Abstract
Keywords
Subject Classifications
References
[1] D. Stinson and M. Paterson, Cryptography: Theory and Practice, ser. Textbooks in Mathematics, vol. 2. Chapman and Hall/CRC Press (2018). [Online]. Available: https://books.google.co.in/books?id=nHxqDwAAQBAJ.
[2] C. E. Shannon, “Communication theory of secrecy systems,” Bell System Technical Journal, vol. 28, no. 4, pp. 656–715, 1949. [Online]. Available: https://onlinelibrary.wiley.com/doi/abs/10.1002/j.1538-7305.1949.tb00928.x.
[3] V. Taghvayi-Yazdelli and M. Ghorbani, “Characterization of bipartite cayley graphs in terms of boolean functions,” Journal of Information and Optimization Sciences, vol. 39, no. 7, pp. 1567–1582 (2018). [Online]. Available: https://doi.org/10.1080/02522667.2017.1384181.
[4] P. Priyadarsini, “A survey on some applications of graph theory in cryptography,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 18, no. 3, pp. 209–217 (2015). [Online]. Available: https://doi.org/10.1080/09720529.2013.878819.
[5] O. Wardak, D. Sinha, and A. Sethi, “Encryption and decryption of signed graph matrices through RSA algorithm,” Indian Journal of Pure and Applied Mathematics (2023). [Online]. Available: https://doi.org/10.1007/s13 226–023–00 452–9.
[6] W. Al Etaiwi, “Encryption algorithm using graph theory,” Journal of Scientific Research and Reports, vol. 3, pp. 2519–2527 (2014).
[7] V. A. Ustimenko, “Graphs with special arcs and cryptography,” Acta Applicandae Mathematica, vol. 74, pp. 117–153 (2002).
[8] M. Ghorbani and F. N. Larki, “On the spectrum of finite cayley graphs,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 21, no. 1, pp. 83–112 (2018). [Online]. Available: https://doi.org/10.1080/09720529.2018.1449797.
[9] A. Sethi, D. Sinha, and O. Wardak, “Algorithmic approach to find s-consistency in common-edge signed graph,” MethodsX, vol. 9, p. Article ID 101783 (2022). [Online]. Available: https://www.sciencedirect.com/science/article/pii/S2215016122001637.
[10] S. G. Akl and I. Assem, “Fully homomorphic encryption: a general framework and implementations,” International Journal of Parallel, Emergent and Distributed Systems, vol. 35, no. 5, pp. 493–498 (2020). [Online]. Available: https://doi.org/10.1080/17445760.2018.1553041.
[11] C. Gentry, “Computing arbitrary functions of encrypted data,” Communications of the Association for Computing Machinery (ACM), vol. 53, no. 3, pp. 97–105 (Mar. 2010). [Online]. Available: https://doi.org/10.1145/1666420.1666444.
[12] A. Kasten, A. Scherp, F. Armknecht, and M. Krause, “Towards search on encrypted graph data,” Proceedings of the 2013th International Conference on Society, Privacy and the Semantic Web - Policy and Technology, vol. 1121, pp. 46–57 (2013).
[13] Q. Wang, K. Ren, M. Du, Q. Li, and A. Mohaisen, “Secgdb: Graph encryption for exact shortest distance queries with efficient updates,” in Financial Cryptography and Data Security, A. Kiayias, Ed. Cham: Springer International Publishing, pp. 79–97 (2017).
[14] Z. Cao and L. Liu, “On the weakness of fully homomorphic encryption,” ArXiv, vol. abs/1511.05341 (2015). [Online]. Available: http://arxiv.org/abs/1511.05341.
[15] K. E. Makkaoui, A. Ezzati, and A. B. Hssane, “Challenges of using homomorphic encryption to secure cloud computing,” Proceedings of International Conference on Cloud Technologies and Applications (CloudTech), pp. 1–7 (2015).
[16] D. Sinha and A. Sethi, “Encryption using network and matrices through signed graphs,” International Journal of Computer Applications, vol. 138, no. 4, pp. 6–13 (Mar. 2016).
[17] B. Ni, Q. Rabiha, S. U. Rehman, and F. Ghulam, “Some graph-based encryption schemes,” Journal of Mathematics, vol. 2021, p. Article ID 6614172 (Feb. 2021). [Online]. Available: https://ideas.repec.org/a/hin/jjmath/6614172.html.
[18] M. Acharya and D. Sinha, “Common-edge sigraphs,” AKCE International Journal of Graphs and Combinatorics, vol. 3, no. 2, pp. 115–130 (2006). [Online]. Available: https://www.tandfonline.com/doi/abs/10.1080/09728600.2006.12088809.
[19] D. Sinha and P. Garg, “On the unitary Cayley signed graphs,” Electronic Journal of Combinatorics, vol. 18, no. 1, p. Article ID P229 (2011).
[20] G. A. Selim, “How to encrypt a graph,” International Journal of Parallel, Emergent and Distributed Systems, vol. 35, no. 6, pp. 668–681 (2020). [Online]. Available: https://doi.org/10.1080/17445760.2018.1550771.
[21] S. G. Akl, “The graph is the message: design and analysis of an unconventional cryptographic function,” in From Parallel to Emergent Computing, CRC Press, pp. 425–442 (2019).
[22] J. Katz and Y. Lindell, Introduction to Modern Cryptography, ser. Chapman & Hall/CRC Cryptography and Network Security Series. CRC Press (2021). [Online]. Available: https://books.google.co.in/books?id=RsoOEAAAQBAJ.
