iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1007/S11277-022-09557-6
Euler Phi Function and Gamma Function Based Elliptic Curve Encryption for Secured Group Communication | Wireless Personal Communications Skip to main content
Springer Nature Link
Log in

Euler Phi Function and Gamma Function Based Elliptic Curve Encryption for Secured Group Communication

  • Published:
Wireless Personal Communications Aims and scope Submit manuscript

Abstract

In this paper, we propose a new clustering, encryption and trust modeling based energy aware routing secured algorithm for performing secured data communication in Wireless Sensor Networks For this purpose, an Elliptic Curve Cryptography based encryption scheme is proposed in this work where the key generation scheme of Elliptic curve cryptography and the strength of the keys used in it for encryption are enhanced by pre-concatenation and post-concatenation of values obtained from the Euler’s phi function value and Gamma function values based on the user identifier values for ‘n’ different users. This proposed technique performs secured routing by encrypting the messages before they are routed to the destination through the network. In this scheme, only one pairing computation with a loop is necessary to encrypt a single message which is to be communicated to ‘n’ different receivers by forming ‘n’ different cipher texts using the proposed elliptic curve group theory based encryption algorithm. The proposed secured routing algorithm has been modeled in this work by performing the encryption of the plain text message before it is sent in the network. Moreover, this proposed system uses a trust model to check for any attempt by intermediate nodes for decrypting the encrypted messages during routing in order to enhance the security of communication. The proposed encryption scheme reduces the computation cost by computing the keys for all the receivers in one attempt. Performance analysis of this proposed scheme shows that computation time is for key formation, encryption and decryption are less in the proposed scheme when it is compared with the existing ECC based schemes for encryption and decryption. In addition, the secured routing algorithm proposed in this paper that uses the proposed encryption technique and trust modeling for enhancing the security of communication increases the packet delivery ratio, security and the overall network performance and it also decreases the delay and energy consumption by avoiding the security attacks efficiently.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Availability of Data and Material

No such data and material are used in this work.

References

  1. Gurumoorthi, E., & Ayyasamy, A. (2019). Cache agent based location aided routing protocol using direction for performance enhancement in VANET. Wireless Personal Communications, 109(2), 1195–1216.

    Article  Google Scholar 

  2. Munuswamy Selvi, S. V. N., Kumar, S., Ganapathy, S., Ayyanar, A., Nehemiah, H. K., & Kannan, A. (2021). An energy efficient clustered gravitational and fuzzy based routing algorithm in WSNs. Wireless Personal Communications, 116(1), 61–90.

    Article  Google Scholar 

  3. Sumathi, J., & Velusamy, R. L. (2021). A review on distributed cluster based routing approaches in mobile wireless sensor networks. Journal of Ambient Intelligence and Humanized Computing, 12(1), 835–849.

    Article  Google Scholar 

  4. Selvakumar, B. D. L. S. K. (2021). Intelligent energy-aware and secured QoS routing protocol with dynamic mobility estimation for wireless sensor networks. Wireless Networks, 27(2), 1503–1514.

    Article  Google Scholar 

  5. Jiang, X., Sun, C., Cao, L., Law, N.-F., & Loo, K. H. (2022). Semi-decentralized energy routing algorithm for minimum-loss transmission in community energy internet. International Journal of Electrical Power & Energy Systems, 135, 107547.

    Article  Google Scholar 

  6. Diffie, W., & Hellman, M. (1976). New directions in cryptography. IEEE transactions on Information’s theory, 22(6), 644–654.

    Article  MathSciNet  MATH  Google Scholar 

  7. Silverman, G. H. (1985). The arithmetic of elliptic curves. Springer.

    Google Scholar 

  8. Lin, D., & Wang, Q. (2017). A game theory based energy efficient clustering routing protocol for WSNs. Wireless Networks, 23(4), 1101–1111.

    Article  Google Scholar 

  9. Prithi, S., & Sumathi, S. (2021). Automata based hybrid PSO–GWO algorithm for secured energy efficient optimal routing in wireless sensor network. Wireless Personal Communications, 117(2), 545–559.

    Article  Google Scholar 

  10. Vijayakumar, P., Bose, S., & Kannan, A. (2013). Centralized key distribution protocol using the greatest common divisor method. Computers & Mathematics with Applications, 65(9), 1360–1368.

    Article  MathSciNet  MATH  Google Scholar 

  11. Maheshwari, P., Sharma, A. K., & Verma, K. (2021). Energy efficient cluster based routing protocol for WSN using butterfly optimization algorithm and ant colony optimization. Ad-Hoc Networks, 110, 1–13.

    Article  Google Scholar 

  12. Shafiq, M., Ashraf, H., Ullah, A., & Tahira, S. (2020). Systematic literature review on energy efficient routing schemes in WSN – A survey. Mobile Networks and Applications, 25, 882–895.

    Article  Google Scholar 

  13. Murthy, S., Souza, R. J. D., & Varaprasad, G. (2012). Digital signature-based secure node disjoint multipath routing protocol for wireless sensor networks. IEEE Transactions on Sensors Journal, 12(10), 2941–2949.

    Article  Google Scholar 

  14. Shamim Hossain, M., You, X., Xiao, W., Luc, J., & Song, E. (2019). QoS-oriented multimedia transmission using multipath routing. Future Generation Computer Systems, 99, 226–234.

    Article  Google Scholar 

  15. Xiao, J., Liu, Y., Qin, H., Li, C., & Zhou, J. (2021). A novel QoS routing energy consumption optimization method based on clone adaptive whale optimization algorithm in IWSNs. Journal of Sensors, 2021, 1–17. https://doi.org/10.1155/2021/5579252

    Article  Google Scholar 

  16. Logambigai, R., Ganapathy, S., & Kannan, A. (2018). Energy–efficient grid-based routing algorithm using intelligent fuzzy rules for wireless sensor networks. Computers & Electrical Engineering, 68, 62–75.

    Article  Google Scholar 

  17. Ponguwala, M., & Rao, S. (2019). E2-SR: A novel energy-efficient secure routing scheme to protect MANET-IoT. IET Communications, 13(19), 3207–3216.

    Article  Google Scholar 

  18. Maheswari, M., & Karthika, R. A. (2021). A novel QoS based secure unequal clustering protocol with intrusion detection system in wireless sensor networks. Wireless Personal Communications, 118(2), 1535–1557.

    Article  Google Scholar 

  19. Heinzelman, W. R., Chandrakasan, A. P., Balakrishnan (2000). Energy-efficient communication protocol for wireless microsensor networks, Proceedings of IEEE 33rd annual Hawaii International Conference on System Sciences, Vol. 2, pp. 1–10.

  20. Heinzelman, W. R., Chandrakasan, A. P., & Balakrishnan. (2002). An application specific protocol architecture for wireless sensor network. IEEE Transaction on Wireless Communication, 1(4), 660–670.

    Article  Google Scholar 

  21. Younis, O., & Fahmy, S. (2004). HEED: A hybrid, energy-efficient, distributed clustering approach for ad hoc sensor networks. IEEE Transactions on Mobile Computing, 3(4), 366–379.

    Article  Google Scholar 

  22. Rajendran, N., Jawahar, P. K., & Priyadarshini, R. (2019). Cross centric intrusion detection system for secure routing over black hole attacks in MANETs. Computer Communications, 148, 129–135.

    Article  Google Scholar 

  23. Stallings, W. (2005). Cryptography and network security principles and practices. Prentice Hall.

    Google Scholar 

  24. Forouzan, A. (2015). Cryptography and network security. McGraw Hill Education.

    Google Scholar 

  25. Miller, V. S. (1986). Use of elliptic curves in cryptography. In Lecture Notes in Computer Sciences on Advances in cryptology- CRYPTO85. Berlin, Heidelberg: Springer-Verlag. 1986, pp.417–426. URLhttp://dl.acm.org/citation.cfm?id=18262.25413.

  26. Geetha, R., Padmavathy, T., Thilagam, T., & Lallithasree, A. (2020). Tamilian cryptography: An efficient hybrid symmetric key encryption algorithm. Wireless Personal Communications, 112, 21–36.

    Article  Google Scholar 

  27. Sangeetha, G., Vijayalakshmi, M., Ganapathy, S., & Kannan, A. (2020). An improved congestion-aware routing mechanism in sensor networks using fuzzy rule sets. Peer Peer Networking and Applications, 13(3), 890–904.

    Article  Google Scholar 

  28. Koblitz, N. (1978). Elliptic curve cryptosystem. Mathematics of Computation, 48(177), 203–209.

    Article  MathSciNet  MATH  Google Scholar 

  29. Jr Hendrik, W. L. (1987). Factoring integers with elliptic curves. Annals of Mathematics, 126(2), 649–673.

    MathSciNet  MATH  Google Scholar 

  30. Peyravian, M., Matyas, S. M., & Zunic, N. (1999). Decentralized group key management for secure multicast communications. Computer Communications, 22(13), 1183–1187.

    Article  Google Scholar 

  31. Bill Hancock CISSP. (1999). Elliptical curve cryptography and standards for efficient cryptography group. Computers & Security, 18(1), 4–15.

    Article  Google Scholar 

  32. Lin, Y.-L., & Hsu, C.-L. (2011). Secure key management scheme for dynamic hierarchical access control based on ECC. Journal of Systems and Software, 84(4), 679–685.

    Article  MathSciNet  Google Scholar 

  33. Fan, D., Meng, X. F., Wang, Y., Yang, X., Peng, X., He, W., Dong, G., & Chen, H. (2013). Asymmetric cryptosystem and software design based on two-step phase-shifting interferometry and elliptic curve algorithm. Optics Communications, 309, 50–56.

    Article  Google Scholar 

  34. Vijayakumar, P., Bose, S., & Kannan, A. (2014). Chinese remainder theorem based centralised group key management for secure multicast communication. IET information Security, 8(3), 179–187.

    Article  Google Scholar 

  35. Daghighi, B., Kiah, M. L. M., Shamshirband, S., Iqbal, S., & Asghari, P. (2015). Key management paradigm for mobile secure group communications: Issues, solutions, and challenges. Computer Communications, 72, 1–16.

    Article  Google Scholar 

  36. Vijayakumar, P., Azees, M., Kannan, A., & Deborah, L. J. (2016). Dual authentication and key management techniques for secure data transmission in vehicular ad hoc networks. IEEE Transactions on Intelligent Transportation Systems, 17(4), 1015–1028.

    Article  Google Scholar 

  37. Liu, Y., Liu, Y., Dong, M., Ota, K., & Liu, A. (2016). ActiveTrust: Secure and trustable routing in wireless sensor networks. IEEE Transactions on Information Forensics and Security, 11(9), 2013–2027.

    Article  Google Scholar 

  38. Liu, Z., Huang, X., Hu, Z., Khan, M. K., Seo, H., & Zhou, L. (2017). On emerging family of elliptic curves to secure Internet of Things: ECC comes of age. IEEE Transactions on Dependable and Secure Computing, 14(3), 237–248.

    Google Scholar 

  39. Santhosh Kumar, S. V. N., & Palanichamy, Y. (2018). Energy efficient and secured distributed data dissemination using hop by hop authentication in WSN. Wireless Networks, 24(4), 1343–1360.

    Article  Google Scholar 

  40. Kalidoss, T., Rajasekaran, L., Kanagasabai, K., Sannasi, G., & Kannan, A. (2020). QoS aware trust based routing algorithm for wireless sensor networks. Wireless Personal Communications, 110(4), 1637–1658.

    Article  Google Scholar 

  41. Kumar, V., Kumar, R., & Pandey, S. K. (2020). A computationally efficient centralized group key distribution protocol for secure multicast communications based upon RSA public key cryptosystem. Journal of King Saud University - Computer and Information Sciences, 32(9), 1081–1094.

    Article  Google Scholar 

  42. Wang, L., Tian, Y., Zhang, D., & Yanhua, Lu. (2019). Constant-round authenticated and dynamic group key agreement protocol for D2D group communications. Information Sciences, 503, 61–71.

    Article  MathSciNet  MATH  Google Scholar 

  43. Viswanathan, S., & Kannan, A. (2019). Elliptic key cryptography with beta gamma function for secure routing in wireless sensor networks. Wireless Networks, Springer Publication., 25(8), 4903–4914.

    Article  Google Scholar 

  44. Sethuraman, P., Tamizharasan, P. S., & Arputharaj, K. (2019). Fuzzy genetic elliptic curve Diffie Hellman algorithm for secured communication in networks. Wireless Personal Communications, 105(3), 993–1007.

    Article  Google Scholar 

  45. Selvi, M., Thangaramya, K., Ganapathy, S., Kulothungan, K., Nehemiah, H. K., & Kannan, A. (2019). An energy aware trust based secure routing algorithm for effective communication in wireless sensor networks. Wireless Personal Communications, 105(4), 1475–1490.

    Article  Google Scholar 

  46. Prabhu Kavin, B., & Ganapathy, S. (2019). A secured storage and privacy-preserving model using CRT for providing security on cloud and IoT-based applications. Computer Networks, 151, 181–190.

    Article  Google Scholar 

  47. Abbasinezhad-Mood, D., Ostad-Sharif, A., Nikooghadam, M., & Mazinani, S. M. (2020). A secure and efficient key establishment scheme for communications of smart meters and service providers in smart grid. IEEE Transactions on Industrial Informatics, 16(3), 1495–1502. https://doi.org/10.1109/TII.2019.2927512

    Article  Google Scholar 

  48. Kurt, G. K., Khosroshahi, Y., Ozdemir, E., Tavakkoli, N., & Topal, O. A. (2020). A hybrid key generation and a verification scheme. IEEE Transactions on Industrial Informatics, 16(1), 703–714. https://doi.org/10.1109/TII.2019.2950465

    Article  Google Scholar 

  49. Gharsallah, I., Smaoui, S., & Zarai, F. (2020). An efficient authentication and key agreement protocol for a group of vehicles devices in 5G cellular networks. IET Information Security, 14(1), 21–29.

    Article  Google Scholar 

  50. Shin, S., & Kwon, T. (2020). A privacy-preserving authentication, authorization, and key agreement scheme for wireless sensor networks in 5G-integrated Internet of Things. IEEE Access, 8, 67555–67571. https://doi.org/10.1109/ACCESS.2020.2985719

    Article  Google Scholar 

  51. Dang, T. K., Pham, C. D. M., & Nguyen, T. L. P. (2020). A pragmatic elliptic curve cryptography-based extension for energy-efficient device-to-device communications in smart cities. Sustainable Cities and Society, 56, 102097.

    Article  Google Scholar 

  52. Elhoseny, M., Elminir, H., Riad, A., & Yuan, X. (2016). A secure data routing schema for WSN using elliptic curve cryptography and homomorphic encryption. Journal of King Saud University - Computer and Information Sciences, 28(3), 262–275.

    Article  Google Scholar 

  53. Ahmed, A., Bakar, K. A., Channa, M. I., Haseeb, K., & Khan, A. W. (2016). A trust aware routing protocol for energy constrained wireless sensor network. Telecommunication Systems, 61(1), 123–140.

    Article  Google Scholar 

  54. Mazinani, A., Mazinani, S. M., & Mirzaie, M. (2019). FMCR-CT: An energy-efficient fuzzy multi-cluster based routing with a constant threshold in wireless sensor network. Alexandria Engineering Journal, 58(1), 127–141.

    Article  Google Scholar 

  55. Ayyasamy, A., & Venkatachalapathy, K. (2015). Context aware adaptive fuzzy based QoS routing scheme for streaming services over MANETs. Wireless Networks, 21(2), 421–430.

    Article  Google Scholar 

  56. Beheshtiasl, A., & Ghaffari, A. (2019). Secure and trust-aware routing scheme in wireless sensor networks. Wireless Personal Communication, 107(4), 1799–1804.

    Article  Google Scholar 

  57. Smart, Nigel P. (1999). The discrete logarithm on elliptic curves of trace one. Journal of cryptology, 12, 193–196.

    Article  MathSciNet  MATH  Google Scholar 

  58. Andrews, G. E. Askey, R. & Roy, R. (1999). Special Functions. In: Encyclopedia of mathematics and its application, Vol.71

  59. Broker, R., & Stevenhagen, P. (2007). Efficient CM-construction of elliptic curves over finite field. Mathematics of Computation, 76(260), 2161–2179.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

No funding is received for this work from anywhere.

Author information

Authors and Affiliations

  1. Department of Information Science and Technology, CEG Campus, Anna University, Chennai, India

    S. Viswanathan

  2. Ramanujan Computing Centre, CEG Campus, Anna University, Chennai, India

    R. S. Bhuvaneswaran

  3. Centre for Cyber-Physical Systems & SCOPE, Vellore Institute of Technology, Chennai, India

    Sannasi Ganapathy

  4. School of Computer Science and Engineering, Vellore Institute of Technology, Vellore, India

    A. Kannan

Authors
  1. S. Viswanathan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. S. Bhuvaneswaran
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sannasi Ganapathy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. Kannan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Kannan.

Ethics declarations

Conflicts of interest

There is no conflict of interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Viswanathan, S., Bhuvaneswaran, R.S., Ganapathy, S. et al. Euler Phi Function and Gamma Function Based Elliptic Curve Encryption for Secured Group Communication. Wireless Pers Commun 125, 421–451 (2022). https://doi.org/10.1007/s11277-022-09557-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11277-022-09557-6

Keywords

Search

Navigation