150 Int. J. Trust Management in Computing and Communications, Vol. 2, No. 2, 2014 Copyright © 2014 Inderscience Enterprises Ltd. A deterministic key pre-distribution scheme for WSN using projective planes and their complements Sarbari Mitra*, Ratna Dutta and Sourav Mukhopadhyay Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal, Pin 721302, India E-mail: sarbari@maths.iitkgp.ernet.in E-mail: ratna@maths.iitkgp.ernet.in E-mail: sourav@maths.iitkgp.ernet.in *Corresponding author Abstract: We present two deterministic key pre-distribution schemes, one using projective planes and the other using complementary design of projective plane. The nodes are arranged hierarchically through a structure of (p 2 + p)-nary tree, where p is a prime power. Our schemes are incumbent to more efficient resilience compared to the existing schemes. Each node requires storing significantly less number of keys. Furthermore, any number of nodes can be intrinsically inserted in the system by attributing a very few keys to the recently introduced nodes only. More interestingly, such node insertions in our schemes are done without interfering the normal functioning of the existing organised network. Keywords: Steiner system; projective planes; complementary design; key pre-distribution; connectivity; resilience; scalability. Reference to this paper should be made as follows: Mitra, S., Dutta, R. and Mukhopadhyay, S. (2014) ‘A deterministic key pre-distribution scheme for WSN using projective planes and their complements’, Int. J. Trust Management in Computing and Communications, Vol. 2, No. 2, pp.150–184. Biographical notes: Sarbari Mitra received her BSc in 2005 under Calcutta University and MSc degree in 2007 from Indian Institute of Technology Kharagpur. Presently, she is pursuing her PhD at IIT Kharagpur. Ratna Dutta is currently an Assistant Professor in the Department of Mathematics, Indian Institute of Technology, Kharagpur, India. She received her BSc (Mathematics Hons.) and MSc in Applied Mathematics from University of Calcutta, India in 1996 and 1998, respectively. She received her PhD in the area of Cryptology (Computer Science) from Indian Statistical Institute, India in 2006. She visited ENSTA, Paris in 2006 and worked as an Associate Scientist at the Institute for Infocomm Research, Singapore during 2006 to 2008. She was also a Postdoctoral Research Fellow in the Department of Computer Science, National University of Ireland, Maynooth during 2008 to 2010. Her research interests include public key cryptography, elliptic curve cryptosystem and pairings, dynamic group key agreement, password-based protocols, word-based public key cryptography and wireless ad hoc networks.