Many network applications involve data transfer; therefore there is a need to have a secure network, which can be achieved through the use of cryptography. In this paper, we present an innovative algorithm for encryption and decryption using connected graphs. Message represented by a connected graph can be encrypted by using a spanning tree of the graph. Any message represented in the graph is either on a branch or on a chord with respect to the spanning tree. Depending whether it is a branch or a chord graph theorems are applied to the spanning tree for both encryption and decryption purposes. This approach used to encrypt leads to more secure data transfer. © 2012 Taylor &amp; Francis Group, LLC.

Selvakumar R

Department of Mathematics

School of Advanced Sciences

Vellore Campus

Gupta N.

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Fundamental circuits and cut-sets used in cryptography

Journal of Discrete Mathematical Sciences and Cryptography

Cognitive radio networks have emerged as a possible solution for the spectrum scarcity problem. Cognitive radio networks involve heterogeneous entities as part of it for facilitating spectrum sharing. Ensuring reliability and security in such scenario is inevitable for the licensed users (primary users) as well as for the unlicensed users (secondary users). To address the challenges of reliable and secure communication for the secondary users, in this paper, a novel reliable and secure communication framework is proposed. A class of group codes called concatenated kernel codes is used to achieve reliability and techniques of fundamental cutset and fundamental circuit to achieve security in terms of authentication of sender. It is shown that the proposed communication framework provides reliability mitigating the continuous interference of primary users and security by defending against the cryptanalytic attacks such as replay attack, related key attack, and man-in-the-middle attacks. The theoretical basis of the proposed framework is validated, and its performance is evaluated through simulations. Copyright © 2018 John Wiley &amp; Sons, Ltd.

International Journal of Communication Systems

A novel reliable and secure communication scheme for cognitive radio networks using concatenated kernel codes

Ensuring reliability and security has been a challenge in modern communication systems. To achieve these challenges, a novel reliable and secure communication system is designed in this paper. Reliability is achieved by constructing a class of error correcting codes called concatenated kernel codes. Security in terms of source authentication is achieved from using graph nature of trellis employing techniques from graph theory namely fundamental cut-set and fundamental circuit. It has been shown that the proposed communication framework achieves the goal of reliability and security considering the channel noise and cryptanalytic attacks. The theoretical basis of the proposed framework is validated and its performance is evaluated through simulations. © 2018 Inderscience Enterprises Ltd.

International Journal of Information and Computer Security

Reliable and secure communication using fundamental cut-sets and fundamental circuits

Forney's representation of Trellis code received wide attention by researchers and engineers with its simplicity in representing codes and elegant nature to analyze codes with sys- tem theoretic properties, graph theoretic properties with efficient encoding and decoding procedures. In this paper, we consider the connected graph nature of trellis and propose security feature over Trellis using fundamental cut-set and fundamental circuits principle. We use the graph theoretic approach, by generating limited spanning trees of trellis, fundamental cut-sets and fundamental circuits, private key cryptosystem is defined in which fundamental cut-set acts as a key to encrypt and decrypt. We have used a class of group codes called Kernel codes and its trellis, to show that private key cryptosystem can be used over Trellis and fundamental cut-set acts as a key to encrypt and decrypt message at sender and receiver respectively. © 2015 IEEE.

2015 International Conference on Smart Technologies and Management for Computing, Communication, Controls, Energy and Materials (ICSTM)

Secure communication over Trellis: Graph theoretic approach

Trellis representation of codes helps in analyzing and understanding the nature of the codes. Trellis has the connected graph nature where all paths from the 'root' vertex to 'goal' vertex forms the codewords. Efficient encoding and decoding algorithms are existing for communication over trellis. In the conventional communication system, Trellis is constructed for the encoded message at the sender and the algorithm such as Viterbi is used to decode the encoded message at the receiver. Any receiver with such decoding mechanism can be able to decode the message, which gives the chance for the intruder to get the message making the communication insecure. In this paper we propose a reliable and secure communication system which provides reliability by the Error Correction Techniques and Security by the graph based Cryptosystem. Using such system intruder's access to the informa- tion can be avoided and also if any errors occurred during transmission over noisy channel can be corrected. We have used Kernel codes and it's Trellis representation to demonstrate the construction of reliable and secure cryptosystem. © 2015 The Authors.

Journal	Journal of Discrete Mathematical Sciences and Cryptography
Publisher	Informa UK Limited
ISSN	0972-0529
Open Access	0