Logical Key Hierarchy is a scalable and efficient method to achieve logarithmic rekeying cost in secure group communication. In applications like pay per view, video conferencing with multiple rekeying operations, the key tree will be unbalanced and will generate worst case rekeying cost. With each join, leave operation we change group key, as well as update all keys along the key path of join/leave user. Key aspect in secure group communication is maintained balanced key tree and achieving logarithmic rekeying cost. In this paper improvement in Non-split balancing high order tree is proposed. I-NSBHO (improved Non Split Balancing High order tree) with proposed Join user algorithm and leave user algorithm maintains balance of tree and always achieve logarithmic rekeying cost. Our experimental result shows the achieved improvement in rekeying cost of I-NSBHO join and leave operations compared to original NSBHO join and leave operations. With Node pruning I-NSBHO improves join cost and maintains logarithmic Rekeying cost for leave operation

Secure Group Communication, NSBHO Tree, Logical Key Hierarchy, Message cost, Rekeying, Key tree, key path, Logarithmic Rekeying Cost)

[1] Takahito Sakamoto, Takashi Tsuji, Yuichi Kaji. "Group key rekeying using the LKH tech-nique and the Huffman algorithm" , 2008 International Symposium on Information Theory and Its Applications, 2008
[2] Kuei-Yi Chou, Yi-Ruei Chen, Wen-Guey Tzeng. "An efficient and secure group key man-agement scheme supporting frequent key updates on Pay-TV systems" , 2011 13th Asia-Pacific Network Operations and Management Symposium, 2011
[3] H. Lu. "A novel high-order tree for secure multicast key management" , IEEE Transactions on Computers, 2/2005
[4] H. Zhou, M. Zheng and T. Wang, “A Novel Group Key scheme for MANETS”, Advanced in control Engineering and Information Science, Procedia Engineering, IJSIA, 2011, pp. 3388-3395.
[5] S. Zhao, R. Kent and A. Aggarwal, “A Key Management and secure routing integrated framework for Ad-hoc Networks”, Ad-hoc Networks, Elsevier, vol-11, 2013, pp. 1046-1061
[6] Hanatani, Yoshikazu, et al. Secure Multicast Group Management and Key Distribution in IEEE 802.21. Security Standardisation Research Springer International Publishing. 2016, pp. 227-243.
[7] S.K. Hafizul Islam, G.P. Biswas A pairing-free identity-based two-party authenticated key agreement protocol for secure and efficient communication J. King Saud Univ.-Comput. Inf. Sci., 29 (1) (2017), pp. 63-73
[8] Vinod Kumar, Rajendra Kumar, S.K. Pandey, "A computationally efficient centralized group key distribution protocol for secure multicast communications based upon RSA pub-lic key cryptosystem", Journal of King Saud University - Computer and Information Sciences, 2018.
[9] Aparna S. Pande Y. V. Joshi, Manisha Y. Joshi, “Analysis on Logical Key Hierarchy and Variants for Secure Group Communication”, ICCASP 2018, Book chapter, Springer-Atalntis, AISR, ISSN 1951-6851.
[10] J. Goshi and R.E. Ladner, “Algorithms for Dynamic Multicast Key Distribution Trees,” Proc ACM Symp. Principles of Distributed Computing (PODC 2003), 2003.
[11] C. K. Wong, M. Gauda and S. S. Lam, “Secure Group Communications Using Key Graphs,” IEEE/ACM Transactions on Networking, Vol.8, no.1, pp.16-30, 2000.
[12] P.Vijayakumar, S.Bose, A.Kannan, “Centralized key distribution protocol using the great-est common divisor method”, Computers and Mathematics with Applications , volume 65 1360–1368, 2013