MESSAGE EMBEDDED CIPHER USING 2-D CHAOTIC MAP

MESSAGE EMBEDDED CIPHER USING 2-D CHAOTIC MAP

Mina Mishra1 and Dr. V.H. Mankar2 

1Ph. D. Scholar, Department of Electronics & Telecommunication, Nagpur University, Nagpur, Maharashtra, India

2 Senior Faculty, Department of Electronics Engineering, Government Polytechnic, Nagpur, Maharashtra, India 

ABSTRACT

This paper constructs two encryption methods using 2-D chaotic maps, Duffings and Arnold’s cat maps respectively. Both of the methods are designed using message embedded scheme and are analyzed for their validity, for plaintext sensitivity, key sensitivity, known plaintext and brute-force attacks. Due to the less key space generally many chaotic cryptosystem developed are found to be weak against Brute force attack which is an essential issue to be solved. For this issue, concept of identifiability proved to be a necessary condition to be fulfilled by the designed chaotic cipher to resist brute force attack, which is a basic attack. As 2-D chaotic maps provide more key space than 1-D maps thus they are considered to be more suitable. This work is accompanied with analysis results obtained from these developed cipher. Moreover, identifiable keys are searched for different input texts at various key values. The methods are found to have good key sensitivity and possess identifiable keys thus concluding that they can resist linear attacks and brute-force attacks. 

KEYWORDS 

Message embedded scheme, Arnolds Cat map, Duffings map, Identifiability. 

1. INTRODUCTION 

For last several years many efforts have been made to use chaotic systems for enhancing some features of communications systems. Chaotic signals are highly unpredictable and random-like nature, which is the most attractive feature of deterministic chaotic systems that may lead to novel (engineering) applications. Some of the common features between chaos and cryptography [1] [2] are being sensitivity to variables and parameters changes. An important difference between chaos and cryptography lies on the fact that systems used in chaos are defined only on real numbers, while cryptography deals with systems defined on finite number of integers. Nevertheless, we believe that the two disciplines can benefit from each other. Thus, for example, as it is shown in this paper, new encryption algorithms can be derived from chaotic systems. On the other hand, chaos theory may also benefit from cryptography: new quantities and techniques for chaos analysis may be developed from cryptography. During the past two decades, there has been tremendous interest worldwide in the possibility of using chaos in communication systems [3][4]. Many different chaos-based decryption algorithms have been proposed up to date. The aim of this paper is to construct and crypt analyze two of the stream symmetric chaotic ciphers[5] constructed using one of the latest chaotic scheme known as message-embedded 

scheme [6] [7]. Both of the developed methods use 2-D chaotic maps, Duffings and Arnolds Cat map. Parameters of the respective chaotic maps act as secret key in the ciphers due to which complexity and key space is increased compared to 1-D chaotic map. Both of the ciphers are analyzed for key space, avalanche effect and strength against Brute-force and Known-plaintext attack.

A cryptanalytic method based on the identifiability concept, solves the problem of less key space in chaotic ciphers. It is possible to test about the cipher strength against Brute-force attack using it. Both of the mentioned ciphers are concluded to provide security against the Brute-force attack[8]. Identifiability concept fulfils the necessary condition but not sufficient as the developed cryptosystems must be tested for sensitivity and other statistical tests to result in a robust cipher. Thus both the ciphers are tested for sensitivity and it is concluded that some of the keys selected from domain of key space[9] of the ciphers seem to have good key sensitivity and resist known plaintext attack for the available first two characters of plaintext [10] [11]. 

This paper is organized into five sections as follows. Section II, presents the background and in section III algorithm for encryption used in developing ciphers is provided. Then in section IV, analysis result in tabulated form and discussions are presented. Section V, discusses about the conclusions derived.  

2. BACKGROUND 

Message-Embedded Scheme: According to this scheme at the transmitter side, the plain text is encrypted by an encryption rule which uses non-linear function and the state generated by the chaotic system in the transmitter. The scrambled output signal is used further to drive the chaotic system such that the chaotic dynamics is changed continuously in a very complex way. Then another state variable of the chaotic system in the transmitter is transmitted through the channel. At the receiver side, the reconstruction of the plaintext is done by decrypting the input by using the reverse of encryption method.  

Arnold’s Cat Map: Arnolds Cat map is a 2-D discrete-time dynamical system, which takes a point(x, y) in the plane and maps it to a new point using equations:

x(k + )1 = (a − )1 mod[2x(k) + y(k),N]; 

y(k + )1 = mod[x(k) + 1( − b) y(k), N]; 

a, b and N are parameters on which the map depends. At a=0.3, b=0.345, map exhibits chaotic nature.