Elliptic curve and pseudo-inverse matrix based cryptosystem for wireless sensor networks

International Journal of Electrical and Computer Engineering (IJECE) Vol. 9, No. 5, October 2019, pp. 4479~4492 ISSN: 2088-8708, DOI: 10.11591/ijece.v9i5.pp4479-4492  4479 Elliptic curve and pseudo-inverse matrix based cryptosystem for wireless sensor networks Shomen Deb, Md. Mokammel Haque Department of Computer Science and Engineering, Chittagong University of Engineering and Technology, Bangladesh Article Info ABSTRACT Article history: Applying asymmetric key security to wireless sensor network (WSN) has been challenging task for the researcher of this field. One common trade-off is that asymmetric key architecture does provide good enough security than symmetric key but on the other hand, sensor network has some resource limitations to implement asymmetric key approach. Elliptic curve cryptography (ECC) has significant advantages than other asymmetric key system like RSA, D-H etc. The most important feature of ECC is that it has much less bit requirement and at the same time, ensures better security compared to others. Hence, ECC can be a better option for implementing asymmetric key approach for sensor network. We propose a new cryptosystem which is based on Pseudo-inverse matrix and Elliptic Curve Cryptography. We establish a relationship between these two different concepts and evaluate our proposed system on the basis of the results of similar works as well as our own simulation done in TinyOS environment. Received Feb 14, 2019 Revised May 23, 2019 Accepted Jun 11, 2019 Keywords: Discrete Logarithm Problem (DLP) Elliptic Curve Cryptography (ECC) Pseudo-inverse Public key Cryptography (PKC) Wireless Sensor Network (WSN) Copyright © 2019 Institute of Advanced Engineering and Science. All rights reserved. Corresponding Author: Shomen Deb, Department of Computer Science and Engineering, Chittagong University of Engineering and Technology, Kaptai Highway, Raozan, Chittagong 4340, Bangladesh. Email: 1. INTRODUCTION There was a believe that due to resource limitations, PKC is not feasible in WSN to ensure security. Some recent works on public key cryptography have shown reasonable performance on wireless sensor network. With the current generation sensor, asymmetric approach is feasible in terms of both software and hardware perspective. PKC like ECC is very much achievable on 8 bit energy constrained platforms (MICA2, MICA2DOT motes using Atmel Atmega128L). In [1], it is stated that D. Nikam and V. Raut utilized ECC and Enhanced Adaptive Acknowledgment (EAACK) to improve the security of MANETs. V. L. Shivraj et al. reviewed the suitability of onetime passwords for IoT devices then developed a scheme using identity based ECC and Lamport’s OTP algorithm. A. Dua et al. have proposed a scheme for secure smart city vehicle message communication. G. Sahebi et al. have designed a framework utilizing ECC for its fast speed, smaller keys, and greater security for E-health applications such as sensors and wearables. R. Fujdiak et al [2] has done analysis on 60 curves of different international standards and they emphasize on the importance of parameterization of ECC for performance issues. They showed that even 10-50 % execution time reduction can be possible on the prime field. We have seen the implementation of the Diffie-Hellman algorithm over EC on low power devices which is used in power grid and smart grid networks [3]. Their method can be used for key distribution over public channel. As per our future predictions, ECC will play the leading role especially in wireless sensor network genre. By dint of the contribution of many researchers, we can now say that asymmetric key approach can be implemented in sensor network.There are many ideas presented earlier to implement asymmetric key in sensor network. Among those, a pseudo-inverse matrix based key handshaking scheme in asymmetric Journal homepage: http://iaescore.com/journals/index.php/IJECE 4480  ISSN: 2088-8708 manner for WSN, is proposed in [4]. The system mostly depends on TTP (Trusted Third Party) which is used to do major calculations. Their scheme is asserted to be more secure than Diffie-Hellman key exchange protocol and all the calculations are based on linear calculation. One year later in [5], Abedelaziz Mohaisen et al. raised an issue of security in that scheme since base station can be impersonated by any malicious entity and existence of TTP in WSN will be at high cost. In some cases, deployment of TTP seems to be challenging especially in hostile and adversarial environment. Our contribution in this paper are as follows: first, we propose a new asymmetric cryptosystem which is mainly based on ECC and pseudo-inverse matrix algorithm. In terms of initial setup, participating nodes have to have common EC settings as they need to choose random point on EC and derive line equation to get pseudo-inverse matrix. This leads us to set up a unique relation between ECC and pseudo-inverse matrix. Second, we eliminate any base node requirement in our design. Third, rather than working on plain text like [6], we emphasize on secure code used to encrypt the message. The rest of the paper is organized as follows: Related Works – Preliminaries - Proposed System – Implementation of the proposed cryptosystem - Performance and Evaluation – Security Analysis – Conclusion. 2. RELATED WORKS Gupta et al [7] showed that ECC is not only feasible for sensor node but also enables the creation of a complete, secure web server stack that runs efficiently with very stringent resource constraints. Piotrowski et al [8] investigated four types of nodes; MICA2DOT, MICA2, MICAz, and TelosB, and estimated the power consumption for most common RSA and ECC operations. Roman and Alcaraz [9] discussed the applicability of public key infrastructures to wireless sensor networks and Ugus et. al. [10] implement elliptic curve and finite field arithmetic operations on a MICAz mote, which is a typical device employed in wireless sensor networks.Moreover, ECC has significant advantages over another popular PKC called RSA (Rivest-Shamir-Adleman). In [11], ECC-160 provides equivalent security to RSA-1024. Although, to emphasize on data security more, it is recommended to use ECC-224 which is equivalent to RSA-2048. RSA key generation requires generation of large prime numbers whereas ECC generates only random number as private key to build user public key. 3. PRELIMINARIES Before start giving details on our proposed system, we would like to give a brief description about the two concepts (Pseudo-inverse matrix and ECC) which are ultimately the basement of our concept. 3.1. Elliptic curve cryptography ECC (Elliptic Curve Cryptography) has become promising public key cryptography which offers asymmetric approach along with smaller key size, bandwidth savings and faster in implementations while compared to the RSA (Rivest-Shamir-Adleman) cryptography. Integer factorization is the basement of the security of RSA. For simplified ellip (...truncated)